LMFDB - Embedded newform 384.2.v.a.253.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			253.28
Character	$\chi$	$=$	384.253
Dual form			384.2.v.a.85.28

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19979 - 0.748670i) q^{2} +(0.634393 + 0.773010i) q^{3} +(0.878985 - 1.79649i) q^{4} +(3.32465 + 1.00852i) q^{5} +(1.33987 + 0.452498i) q^{6} +(-0.658894 + 0.131062i) q^{7} +(-0.290385 - 2.81348i) q^{8} +(-0.195090 + 0.980785i) q^{9} +O(q^{10})$	\(q+(1.19979 - 0.748670i) q^{2} +(0.634393 + 0.773010i) q^{3} +(0.878985 - 1.79649i) q^{4} +(3.32465 + 1.00852i) q^{5} +(1.33987 + 0.452498i) q^{6} +(-0.658894 + 0.131062i) q^{7} +(-0.290385 - 2.81348i) q^{8} +(-0.195090 + 0.980785i) q^{9} +(4.74393 - 1.27906i) q^{10} +(-4.01341 + 0.395286i) q^{11} +(1.94633 - 0.460218i) q^{12} +(0.0924961 + 0.304919i) q^{13} +(-0.692411 + 0.650541i) q^{14} +(1.32954 + 3.20979i) q^{15} +(-2.45477 - 3.15818i) q^{16} +(-0.921948 + 2.22578i) q^{17} +(0.500218 + 1.32279i) q^{18} +(-1.18894 - 0.635499i) q^{19} +(4.73413 - 5.08624i) q^{20} +(-0.519310 - 0.426187i) q^{21} +(-4.51930 + 3.47898i) q^{22} +(-2.01222 - 3.01150i) q^{23} +(1.99063 - 2.00932i) q^{24} +(5.87886 + 3.92813i) q^{25} +(0.339260 + 0.296589i) q^{26} +(-0.881921 + 0.471397i) q^{27} +(-0.343706 + 1.29890i) q^{28} +(-0.170668 + 1.73283i) q^{29} +(3.99824 + 2.85569i) q^{30} +(0.247500 - 0.247500i) q^{31} +(-5.30964 - 1.95133i) q^{32} +(-2.85164 - 2.85164i) q^{33} +(0.560233 + 3.36070i) q^{34} +(-2.32277 - 0.228773i) q^{35} +(1.59049 + 1.21257i) q^{36} +(-4.20593 - 7.86874i) q^{37} +(-1.90225 + 0.127656i) q^{38} +(-0.177027 + 0.264939i) q^{39} +(1.87203 - 9.64671i) q^{40} +(9.34151 - 6.24180i) q^{41} +(-0.942136 - 0.122542i) q^{42} +(0.863089 - 1.05168i) q^{43} +(-2.81760 + 7.55751i) q^{44} +(-1.63775 + 3.06402i) q^{45} +(-4.66885 - 2.10667i) q^{46} +(6.15840 + 2.55089i) q^{47} +(0.884017 - 3.90109i) q^{48} +(-6.05019 + 2.50607i) q^{49} +(9.99427 + 0.311595i) q^{50} +(-2.30543 + 0.699344i) q^{51} +(0.629087 + 0.101851i) q^{52} +(1.11288 + 11.2993i) q^{53} +(-0.705198 + 1.22584i) q^{54} +(-13.7419 - 2.73342i) q^{55} +(0.560074 + 1.81573i) q^{56} +(-0.263005 - 1.32222i) q^{57} +(1.09255 + 2.20680i) q^{58} +(3.13761 - 10.3433i) q^{59} +(6.93501 + 0.432852i) q^{60} +(-10.9249 + 8.96587i) q^{61} +(0.111652 - 0.482244i) q^{62} -0.671803i q^{63} +(-7.83135 + 1.63398i) q^{64} +1.10703i q^{65} +(-5.55630 - 1.28643i) q^{66} +(0.610952 - 0.501396i) q^{67} +(3.18822 + 3.61270i) q^{68} +(1.05138 - 3.46594i) q^{69} +(-2.95811 + 1.46451i) q^{70} +(1.19682 + 6.01682i) q^{71} +(2.81607 + 0.264078i) q^{72} +(5.01139 + 0.996828i) q^{73} +(-10.9373 - 6.29197i) q^{74} +(0.693025 + 7.03640i) q^{75} +(-2.18673 + 1.57732i) q^{76} +(2.59260 - 0.786458i) q^{77} +(-0.0140425 + 0.450405i) q^{78} +(-15.3139 + 6.34322i) q^{79} +(-4.97617 - 12.9756i) q^{80} +(-0.923880 - 0.382683i) q^{81} +(6.53479 - 14.4825i) q^{82} +(-5.70048 + 10.6648i) q^{83} +(-1.22211 + 0.558325i) q^{84} +(-5.30991 + 6.47014i) q^{85} +(0.248165 - 1.90796i) q^{86} +(-1.44776 + 0.967364i) q^{87} +(2.27756 + 11.1769i) q^{88} +(3.08418 - 4.61580i) q^{89} +(0.328984 + 4.90231i) q^{90} +(-0.100908 - 0.188787i) q^{91} +(-7.17884 + 0.967873i) q^{92} +(0.348333 + 0.0343078i) q^{93} +(9.29856 - 1.55008i) q^{94} +(-3.31188 - 3.31188i) q^{95} +(-1.86000 - 5.34232i) q^{96} +(6.58074 - 6.58074i) q^{97} +(-5.38273 + 7.53636i) q^{98} +(0.395286 - 4.01341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{32}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.19979	−	0.748670i	0.848379	−	0.529390i
$2$	1.19979	−	0.748670i	0.848379	−	0.529390i
$3$	0.634393	+	0.773010i	0.366267	+	0.446298i
$3$	0.634393	+	0.773010i	0.366267	+	0.446298i
$4$	0.878985	−	1.79649i	0.439493	−	0.898246i
$5$	3.32465	+	1.00852i	1.48683	+	0.451025i	0.926197	−	0.377039i	$-0.123058\pi$
$5$	3.32465	+	1.00852i	1.48683	+	0.451025i	0.560633	+	0.828064i	$0.310558\pi$
$6$	1.33987	+	0.452498i	0.546999	+	0.184731i
$7$	−0.658894	+	0.131062i	−0.249039	+	0.0495368i	−0.318031	−	0.948080i	$-0.603022\pi$
$7$	−0.658894	+	0.131062i	−0.249039	+	0.0495368i	0.0689924	+	0.997617i	$0.478022\pi$
$8$	−0.290385	−	2.81348i	−0.102666	−	0.994716i
$9$	−0.195090	+	0.980785i	−0.0650301	+	0.326928i
$10$	4.74393	−	1.27906i	1.50016	−	0.404473i
$11$	−4.01341	+	0.395286i	−1.21009	+	0.119183i	−0.682866	−	0.730544i	$-0.739267\pi$
$11$	−4.01341	+	0.395286i	−1.21009	+	0.119183i	−0.527223	+	0.849727i	$0.676767\pi$
$12$	1.94633	−	0.460218i	0.561857	−	0.132854i
$13$	0.0924961	+	0.304919i	0.0256538	+	0.0845693i	0.968833	−	0.247716i	$-0.0796802\pi$
$13$	0.0924961	+	0.304919i	0.0256538	+	0.0845693i	−0.943179	+	0.332286i	$0.892180\pi$
$14$	−0.692411	+	0.650541i	−0.185055	+	0.173865i
$15$	1.32954	+	3.20979i	0.343286	+	0.828765i
$16$	−2.45477	−	3.15818i	−0.613693	−	0.789545i
$17$	−0.921948	+	2.22578i	−0.223605	+	0.539831i	−0.995374	−	0.0960719i	$-0.969372\pi$
$17$	−0.921948	+	2.22578i	−0.223605	+	0.539831i	0.771769	+	0.635903i	$0.219372\pi$
$18$	0.500218	+	1.32279i	0.117902	+	0.311785i
$19$	−1.18894	−	0.635499i	−0.272760	−	0.145793i	0.329346	−	0.944209i	$-0.393172\pi$
$19$	−1.18894	−	0.635499i	−0.272760	−	0.145793i	−0.602106	+	0.798416i	$0.705672\pi$
$20$	4.73413	−	5.08624i	1.05858	−	1.13732i
$21$	−0.519310	−	0.426187i	−0.113323	−	0.0930016i
$22$	−4.51930	+	3.47898i	−0.963519	+	0.741721i
$23$	−2.01222	−	3.01150i	−0.419576	−	0.627940i	0.560124	−	0.828409i	$-0.310754\pi$
$23$	−2.01222	−	3.01150i	−0.419576	−	0.627940i	−0.979700	+	0.200469i	$0.935754\pi$
$24$	1.99063	−	2.00932i	0.406336	−	0.410152i
$25$	5.87886	+	3.92813i	1.17577	+	0.785626i
$26$	0.339260	+	0.296589i	0.0665343	+	0.0581659i
$27$	−0.881921	+	0.471397i	−0.169726	+	0.0907203i
$28$	−0.343706	+	1.29890i	−0.0649543	+	0.245469i
$29$	−0.170668	+	1.73283i	−0.0316923	+	0.321778i	0.966247	+	0.257617i	$0.0829371\pi$
$29$	−0.170668	+	1.73283i	−0.0316923	+	0.321778i	−0.997940	+	0.0641610i	$0.979563\pi$
$30$	3.99824	+	2.85569i	0.729976	+	0.521375i
$31$	0.247500	−	0.247500i	0.0444524	−	0.0444524i	−0.684531	−	0.728984i	$-0.739993\pi$
$31$	0.247500	−	0.247500i	0.0444524	−	0.0444524i	0.728984	+	0.684531i	$0.239993\pi$
$32$	−5.30964	−	1.95133i	−0.938621	−	0.344950i
$33$	−2.85164	−	2.85164i	−0.496407	−	0.496407i
$34$	0.560233	+	3.36070i	0.0960791	+	0.576356i
$35$	−2.32277	−	0.228773i	−0.392621	−	0.0386697i
$36$	1.59049	+	1.21257i	0.265082	+	0.202096i
$37$	−4.20593	−	7.86874i	−0.691451	−	1.29361i	−0.945247	−	0.326355i	$-0.894179\pi$
$37$	−4.20593	−	7.86874i	−0.691451	−	1.29361i	0.253797	−	0.967258i	$-0.418321\pi$
$38$	−1.90225	+	0.127656i	−0.308586	+	0.0207086i
$39$	−0.177027	+	0.264939i	−0.0283469	+	0.0424242i
$40$	1.87203	−	9.64671i	0.295994	−	1.52528i
$41$	9.34151	−	6.24180i	1.45890	−	0.974805i	0.462809	−	0.886458i	$-0.346842\pi$
$41$	9.34151	−	6.24180i	1.45890	−	0.974805i	0.996090	−	0.0883467i	$-0.0281583\pi$
$42$	−0.942136	−	0.122542i	−0.145375	−	0.0189086i
$43$	0.863089	−	1.05168i	0.131620	−	0.160379i	−0.703030	−	0.711160i	$-0.748170\pi$
$43$	0.863089	−	1.05168i	0.131620	−	0.160379i	0.834650	+	0.550781i	$0.185670\pi$
$44$	−2.81760	+	7.55751i	−0.424769	+	1.13934i
$45$	−1.63775	+	3.06402i	−0.244142	+	0.456757i
$46$	−4.66885	−	2.10667i	−0.688385	−	0.310612i
$47$	6.15840	+	2.55089i	0.898296	+	0.372086i	0.783565	−	0.621310i	$-0.213399\pi$
$47$	6.15840	+	2.55089i	0.898296	+	0.372086i	0.114731	+	0.993397i	$0.463399\pi$
$48$	0.884017	−	3.90109i	0.127597	−	0.563074i
$49$	−6.05019	+	2.50607i	−0.864313	+	0.358010i
$50$	9.99427	+	0.311595i	1.41340	+	0.0440662i
$51$	−2.30543	+	0.699344i	−0.322825	+	0.0979278i
$52$	0.629087	+	0.101851i	0.0872387	+	0.0141241i
$53$	1.11288	+	11.2993i	0.152866	+	1.55207i	0.699459	+	0.714673i	$0.253425\pi$
$53$	1.11288	+	11.2993i	0.152866	+	1.55207i	−0.546593	+	0.837399i	$0.684075\pi$
$54$	−0.705198	+	1.22584i	−0.0959653	+	0.166816i
$55$	−13.7419	−	2.73342i	−1.85295	−	0.368575i
$56$	0.560074	+	1.81573i	0.0748430	+	0.242637i
$57$	−0.263005	−	1.32222i	−0.0348359	−	0.175132i
$58$	1.09255	+	2.20680i	0.143459	+	0.289767i
$59$	3.13761	−	10.3433i	0.408482	−	1.34658i	−0.475768	−	0.879571i	$-0.657830\pi$
$59$	3.13761	−	10.3433i	0.408482	−	1.34658i	0.884250	−	0.467014i	$-0.154670\pi$
$60$	6.93501	+	0.432852i	0.895307	+	0.0558810i
$61$	−10.9249	+	8.96587i	−1.39880	+	1.14796i	−0.429211	+	0.903204i	$0.641208\pi$
$61$	−10.9249	+	8.96587i	−1.39880	+	1.14796i	−0.969584	+	0.244758i	$0.921292\pi$
$62$	0.111652	−	0.482244i	0.0141798	−	0.0612451i
$63$		−	0.671803i		−	0.0846392i
$64$	−7.83135	+	1.63398i	−0.978919	+	0.204248i
$65$			1.10703i			0.137311i
$66$	−5.55630	−	1.28643i	−0.683934	−	0.158348i
$67$	0.610952	−	0.501396i	0.0746397	−	0.0612552i	−0.596334	−	0.802737i	$-0.703376\pi$
$67$	0.610952	−	0.501396i	0.0746397	−	0.0612552i	0.670973	+	0.741481i	$0.265876\pi$
$68$	3.18822	+	3.61270i	0.386628	+	0.438104i
$69$	1.05138	−	3.46594i	0.126571	−	0.417250i
$70$	−2.95811	+	1.46451i	−0.353562	+	0.175043i
$71$	1.19682	+	6.01682i	0.142036	+	0.714065i	0.984510	+	0.175328i	$0.0560985\pi$
$71$	1.19682	+	6.01682i	0.142036	+	0.714065i	−0.842474	+	0.538737i	$0.818902\pi$
$72$	2.81607	+	0.264078i	0.331877	+	0.0311219i
$73$	5.01139	+	0.996828i	0.586539	+	0.116670i	0.479434	−	0.877578i	$-0.340842\pi$
$73$	5.01139	+	0.996828i	0.586539	+	0.116670i	0.107105	+	0.994248i	$0.465842\pi$
$74$	−10.9373	−	6.29197i	−1.27144	−	0.731427i
$75$	0.693025	+	7.03640i	0.0800236	+	0.812494i
$76$	−2.18673	+	1.57732i	−0.250835	+	0.180931i
$77$	2.59260	−	0.786458i	0.295455	−	0.0896252i
$78$	−0.0140425	+	0.450405i	−0.00159000	+	0.0509984i
$79$	−15.3139	+	6.34322i	−1.72295	+	0.713668i	−0.723213	+	0.690625i	$0.757336\pi$
$79$	−15.3139	+	6.34322i	−1.72295	+	0.713668i	−0.999734	+	0.0230438i	$0.992664\pi$
$80$	−4.97617	−	12.9756i	−0.556352	−	1.45071i
$81$	−0.923880	−	0.382683i	−0.102653	−	0.0425204i
$82$	6.53479	−	14.4825i	0.721646	−	1.59933i
$83$	−5.70048	+	10.6648i	−0.625709	+	1.17062i	0.346841	+	0.937924i	$0.387254\pi$
$83$	−5.70048	+	10.6648i	−0.625709	+	1.17062i	−0.972550	+	0.232695i	$0.925246\pi$
$84$	−1.22211	+	0.558325i	−0.133343	+	0.0609183i
$85$	−5.30991	+	6.47014i	−0.575941	+	0.701786i
$86$	0.248165	−	1.90796i	0.0267603	−	0.205741i
$87$	−1.44776	+	0.967364i	−0.155216	+	0.103712i
$88$	2.27756	+	11.1769i	0.242789	+	1.19146i
$89$	3.08418	−	4.61580i	0.326922	−	0.489274i	−0.631205	−	0.775616i	$-0.717439\pi$
$89$	3.08418	−	4.61580i	0.326922	−	0.489274i	0.958127	+	0.286342i	$0.0924394\pi$
$90$	0.328984	+	4.90231i	0.0346780	+	0.516749i
$91$	−0.100908	−	0.188787i	−0.0105781	−	0.0197902i
$92$	−7.17884	+	0.967873i	−0.748446	+	0.100908i
$93$	0.348333	+	0.0343078i	0.0361204	+	0.00355755i
$94$	9.29856	−	1.55008i	0.959073	−	0.159879i
$95$	−3.31188	−	3.31188i	−0.339792	−	0.339792i
$96$	−1.86000	−	5.34232i	−0.189835	−	0.545248i
$97$	6.58074	−	6.58074i	0.668173	−	0.668173i	−0.289120	−	0.957293i	$-0.593363\pi$
$97$	6.58074	−	6.58074i	0.668173	−	0.668173i	0.957293	+	0.289120i	$0.0933626\pi$
$98$	−5.38273	+	7.53636i	−0.543738	+	0.761287i
$99$	0.395286	−	4.01341i	0.0397278	−	0.403363i
$100$	12.2243	−	7.10856i	1.22243	−	0.710856i
$101$	10.0551	−	5.37455i	1.00052	−	0.534787i	0.112037	−	0.993704i	$-0.464262\pi$
$101$	10.0551	−	5.37455i	1.00052	−	0.534787i	0.888479	+	0.458917i	$0.151762\pi$
$102$	−2.24245	+	2.56507i	−0.222036	+	0.253980i
$103$	−10.4696	−	6.99555i	−1.03160	−	0.689292i	−0.0800498	−	0.996791i	$-0.525508\pi$
$103$	−10.4696	−	6.99555i	−1.03160	−	0.689292i	−0.951548	+	0.307499i	$0.900508\pi$
$104$	0.831024	−	0.348780i	0.0814886	−	0.0342007i
$105$	−1.29671	−	1.94066i	−0.126546	−	0.189389i
$106$	9.79464	+	12.7235i	0.951339	+	1.23582i
$107$	12.3138	+	10.1057i	1.19042	+	0.976953i	0.999989	−	0.00474748i	$-0.00151118\pi$
$107$	12.3138	+	10.1057i	1.19042	+	0.976953i	0.190432	+	0.981700i	$0.439011\pi$
$108$	0.0716650	+	1.99872i	0.00689597	+	0.192327i
$109$	11.8295	+	6.32298i	1.13306	+	0.605631i	0.927800	−	0.373077i	$-0.121697\pi$
$109$	11.8295	+	6.32298i	1.13306	+	0.605631i	0.205256	+	0.978708i	$0.434197\pi$
$110$	−18.5338	+	7.00859i	−1.76712	+	0.668243i
$111$	3.41441	−	8.24310i	0.324081	−	0.782401i
$112$	2.03135	+	1.75918i	0.191945	+	0.166227i
$113$	−4.83991	−	11.6846i	−0.455300	−	1.09919i	−0.970279	−	0.241989i	$-0.922200\pi$
$113$	−4.83991	−	11.6846i	−0.455300	−	1.09919i	0.514979	−	0.857203i	$-0.327800\pi$
$114$	−1.30545	−	1.38948i	−0.122267	−	0.130136i
$115$	−3.65276	−	12.0416i	−0.340622	−	1.12288i
$116$	2.96299	+	1.82973i	0.275107	+	0.169886i
$117$	−0.317105	+	0.0312321i	−0.0293164	+	0.00288741i
$118$	−3.97926	−	14.7588i	−0.366321	−	1.35866i
$119$	0.315751	−	1.58739i	0.0289448	−	0.145515i
$120$	8.64461	−	4.67271i	0.789142	−	0.426558i
$121$	5.16256	−	1.02690i	0.469324	−	0.0933544i
$122$	−6.39514	+	18.9363i	−0.578989	+	1.71441i
$123$	10.7512	+	3.26133i	0.969400	+	0.294064i
$124$	−0.227083	−	0.662182i	−0.0203927	−	0.0594657i
$125$	4.56336	+	5.56047i	0.408159	+	0.497343i
$126$	−0.502959	−	0.806021i	−0.0448071	−	0.0718061i
$127$	−4.67131			−0.414512			−0.207256	−	0.978287i	$-0.566453\pi$
$127$	−4.67131			−0.414512			−0.207256	+	0.978287i	$0.566453\pi$
$128$	−8.17265	+	7.82354i	−0.722367	+	0.691510i
$129$	1.36050			0.119785
$130$	0.828804	+	1.32821i	0.0726909	+	0.116492i
$131$	11.7415	+	14.3070i	1.02586	+	1.25001i	0.967806	+	0.251696i	$0.0809882\pi$
$131$	11.7415	+	14.3070i	1.02586	+	1.25001i	0.0580497	+	0.998314i	$0.481512\pi$
$132$	−7.62950	+	2.61640i	−0.664063	+	0.227728i
$133$	0.866672	+	0.262902i	0.0751500	+	0.0227965i
$134$	0.357634	−	1.05897i	0.0308948	−	0.0914811i
$135$	−3.40750	+	0.677794i	−0.293271	+	0.0583352i
$136$	6.52991	+	1.94755i	0.559935	+	0.167001i
$137$	2.66391	−	13.3924i	0.227593	−	1.14419i	−0.682851	−	0.730558i	$-0.739260\pi$
$137$	2.66391	−	13.3924i	0.227593	−	1.14419i	0.910444	−	0.413631i	$-0.135740\pi$
$138$	−1.33341	−	4.94553i	−0.113507	−	0.420991i
$139$	3.54297	−	0.348952i	0.300511	−	0.0295978i	0.0533620	−	0.998575i	$-0.483006\pi$
$139$	3.54297	−	0.348952i	0.300511	−	0.0295978i	0.247149	+	0.968977i	$0.420506\pi$
$140$	−2.45267	+	3.97176i	−0.207289	+	0.335675i
$141$	1.93498	+	6.37878i	0.162955	+	0.537190i
$142$	5.94055	+	6.32289i	0.498520	+	0.530605i
$143$	−0.491755	−	1.18720i	−0.0411226	−	0.0992788i
$144$	3.57640	−	1.79147i	0.298033	−	0.149289i
$145$	−2.31501	+	5.58892i	−0.192251	+	0.464135i
$146$	6.75891	−	2.55590i	0.559371	−	0.211528i
$147$	−5.77542	−	3.08703i	−0.476349	−	0.254614i
$148$	−17.8331	+	0.639415i	−1.46587	+	0.0525596i
$149$	8.33834	+	6.84310i	0.683104	+	0.560609i	0.910660	−	0.413156i	$-0.135574\pi$
$149$	8.33834	+	6.84310i	0.683104	+	0.560609i	−0.227556	+	0.973765i	$0.573074\pi$
$150$	6.09943	+	7.92335i	0.498016	+	0.646939i
$151$	−3.27447	−	4.90059i	−0.266472	−	0.398804i	0.673969	−	0.738760i	$-0.264588\pi$
$151$	−3.27447	−	4.90059i	−0.266472	−	0.398804i	−0.940442	+	0.339955i	$0.889588\pi$
$152$	−1.44272	+	3.52959i	−0.117020	+	0.286287i
$153$	−2.00315	−	1.33846i	−0.161945	−	0.108208i
$154$	2.52178	−	2.88459i	0.203211	−	0.232447i
$155$	1.07246	−	0.573243i	0.0861423	−	0.0460440i
$156$	0.320357	+	0.550904i	0.0256491	+	0.0441076i
$157$	0.318875	−	3.23759i	0.0254490	−	0.258388i	−0.974039	−	0.226382i	$-0.927310\pi$
$157$	0.318875	−	3.23759i	0.0254490	−	0.258388i	0.999488	−	0.0320062i	$-0.0101896\pi$
$158$	−13.6245	+	19.0756i	−1.08390	+	1.51757i
$159$	−8.02844	+	8.02844i	−0.636696	+	0.636696i
$160$	−15.6848	−	11.8424i	−1.23999	−	0.936225i
$161$	1.72053	+	1.72053i	0.135597	+	0.135597i
$162$	−1.39496	+	0.232542i	−0.109599	+	0.0182702i
$163$	6.01787	+	0.592708i	0.471356	+	0.0464245i	0.330907	−	0.943663i	$-0.392645\pi$
$163$	6.01787	+	0.592708i	0.471356	+	0.0464245i	0.140449	+	0.990088i	$0.455145\pi$
$164$	−3.00229	−	22.2684i	−0.234440	−	1.73887i
$165$	−6.60477	−	12.3567i	−0.514181	−	0.961965i
$166$	1.14509	+	17.0633i	0.0888759	+	1.32437i
$167$	10.4969	−	15.7098i	0.812277	−	1.21566i	−0.161211	−	0.986920i	$-0.551540\pi$
$167$	10.4969	−	15.7098i	0.812277	−	1.21566i	0.973488	−	0.228739i	$-0.0734602\pi$
$168$	−1.04827	+	1.58483i	−0.0808757	+	0.122272i
$169$	10.7247	−	7.16601i	0.824976	−	0.551231i
$170$	−1.52676	+	11.7382i	−0.117097	+	0.900277i
$171$	0.855238	−	1.04211i	0.0654017	−	0.0796922i
$172$	−1.13069	−	2.47494i	−0.0862141	−	0.188713i
$173$	−8.57003	+	16.0334i	−0.651568	+	1.21900i	0.311630	+	0.950204i	$0.399125\pi$
$173$	−8.57003	+	16.0334i	−0.651568	+	1.21900i	−0.963198	+	0.268794i	$0.913375\pi$
$174$	−1.01277	+	2.24453i	−0.0767781	+	0.170157i
$175$	−4.38838	−	1.81773i	−0.331730	−	0.137407i
$176$	11.1004	+	11.7047i	0.836723	+	0.882277i
$177$	9.98597	−	4.13632i	0.750591	−	0.310905i
$178$	0.244649	−	7.84701i	0.0183372	−	0.588159i
$179$	−6.59746	+	2.00132i	−0.493117	+	0.149585i	−0.527043	−	0.849839i	$-0.676699\pi$
$179$	−6.59746	+	2.00132i	−0.493117	+	0.149585i	0.0339253	+	0.999424i	$0.489199\pi$
$180$	4.06493	+	5.63544i	0.302982	+	0.420041i
$181$	−0.314349	−	3.19164i	−0.0233653	−	0.237232i	−0.999773	−	0.0212978i	$-0.993220\pi$
$181$	−0.314349	−	3.19164i	−0.0233653	−	0.237232i	0.976408	−	0.215935i	$-0.0692798\pi$
$182$	−0.262408	−	0.150957i	−0.0194510	−	0.0111897i
$183$	−13.8614	−	2.75721i	−1.02467	−	0.203819i
$184$	−7.88847	+	6.53583i	−0.581546	+	0.481828i
$185$	−6.04746	−	30.4026i	−0.444618	−	2.23525i
$186$	0.443611	−	0.219624i	0.0325271	−	0.0161036i
$187$	2.82034	−	9.29740i	0.206243	−	0.679893i
$188$	9.99581	−	8.82133i	0.729019	−	0.643361i
$189$	0.519310	−	0.426187i	0.0377743	−	0.0310005i
$190$	−6.45307	−	1.49405i	−0.468155	−	0.108390i
$191$			0.267025i			0.0193212i	0.999953	+	0.00966062i	$0.00307512\pi$
$191$			0.267025i			0.0193212i	−0.999953	+	0.00966062i	$0.996925\pi$
$192$	−6.23124	−	5.01713i	−0.449701	−	0.362080i
$193$			3.35636i			0.241596i	0.992677	+	0.120798i	$0.0385453\pi$
$193$			3.35636i			0.241596i	−0.992677	+	0.120798i	$0.961455\pi$
$194$	2.96869	−	12.8223i	0.213140	−	0.920588i
$195$	−0.855749	+	0.702295i	−0.0612815	+	0.0502924i
$196$	−0.815890	+	13.0719i	−0.0582779	+	0.933709i
$197$	−0.233630	+	0.770177i	−0.0166455	+	0.0548728i	−0.964870	−	0.262729i	$-0.915378\pi$
$197$	−0.233630	+	0.770177i	−0.0166455	+	0.0548728i	0.948224	+	0.317602i	$0.102878\pi$
$198$	−2.53046	−	5.11118i	−0.179832	−	0.363236i
$199$	−1.23322	−	6.19981i	−0.0874206	−	0.439493i	−0.999561	−	0.0296159i	$-0.990572\pi$
$199$	−1.23322	−	6.19981i	−0.0874206	−	0.439493i	0.912141	−	0.409877i	$-0.134428\pi$
$200$	9.34459	−	17.6807i	0.660762	−	1.25022i
$201$	0.775168	+	0.154191i	0.0546761	+	0.0108758i
$202$	8.04019	−	13.9762i	0.565706	−	0.983365i
$203$	−0.114655	−	1.16412i	−0.00804723	−	0.0817049i
$204$	−0.770071	+	4.75640i	−0.0539158	+	0.333015i
$205$	37.3523	−	11.3307i	2.60880	−	0.791370i
$206$	−17.7986	−	0.554915i	−1.24009	−	0.0386628i
$207$	3.34619	−	1.38604i	0.232577	−	0.0963364i
$208$	0.735932	−	1.04063i	0.0510277	−	0.0721544i
$209$	5.02289	+	2.08055i	0.347440	+	0.143915i
$210$	−3.00869	−	1.35758i	−0.207619	−	0.0936816i
$211$	13.4497	−	25.1626i	0.925913	−	1.73226i	0.296817	−	0.954934i	$-0.404075\pi$
$211$	13.4497	−	25.1626i	0.925913	−	1.73226i	0.629096	−	0.777327i	$-0.283425\pi$
$212$	21.2772	+	7.93260i	1.46133	+	0.544813i
$213$	−3.89181	+	4.74218i	−0.266662	+	0.324929i
$214$	22.3398	+	2.90570i	1.52712	+	0.198629i
$215$	3.93011	−	2.62602i	0.268032	−	0.179093i
$216$	1.58236	+	2.34438i	0.107666	+	0.159515i
$217$	−0.130639	+	0.195514i	−0.00886832	+	0.0132724i
$218$	18.9267	−	1.27013i	1.28188	−	0.0860241i
$219$	2.40863	+	4.50624i	0.162760	+	0.304503i
$220$	−16.9895	+	22.2845i	−1.14543	+	1.50242i
$221$	−0.763959	−	0.0752434i	−0.0513895	−	0.00506142i
$222$	−2.07480	−	12.4462i	−0.139252	−	0.835337i
$223$	5.66559	+	5.66559i	0.379396	+	0.379396i	0.870884	−	0.491488i	$-0.163547\pi$
$223$	5.66559	+	5.66559i	0.379396	+	0.379396i	−0.491488	+	0.870884i	$0.663547\pi$
$224$	3.75424	+	0.589830i	0.250841	+	0.0394096i
$225$	−4.99956	+	4.99956i	−0.333304	+	0.333304i
$226$	−14.5548	−	10.3955i	−0.968168	−	0.691499i
$227$	0.0292558	−	0.297039i	0.00194177	−	0.0197152i	−0.994165	−	0.107870i	$-0.965597\pi$
$227$	0.0292558	−	0.297039i	0.00194177	−	0.0197152i	0.996107	+	0.0881548i	$0.0280970\pi$
$228$	−2.60653	−	0.689721i	−0.172622	−	0.0456779i
$229$	−17.2366	+	9.21316i	−1.13903	+	0.608823i	−0.929442	−	0.368967i	$-0.879711\pi$
$229$	−17.2366	+	9.21316i	−1.13903	+	0.608823i	−0.209585	+	0.977790i	$0.567211\pi$
$230$	−13.3977	−	11.7126i	−0.883418	−	0.772306i
$231$	2.25267	+	1.50519i	0.148215	+	0.0990340i
$232$	4.92483	−	0.0230134i	0.323331	−	0.00151090i
$233$	−6.48007	−	9.69810i	−0.424523	−	0.635344i	0.556130	−	0.831095i	$-0.312286\pi$
$233$	−6.48007	−	9.69810i	−0.424523	−	0.635344i	−0.980654	+	0.195751i	$0.937286\pi$
$234$	−0.357076	+	0.274879i	−0.0233428	+	0.0179694i
$235$	17.9019	+	14.6917i	1.16779	+	0.958383i
$236$	−15.8238	−	14.7283i	−1.03004	−	0.958731i
$237$	−14.6184	−	7.81370i	−0.949568	−	0.507555i
$238$	−0.809595	−	2.14092i	−0.0524782	−	0.138775i
$239$	−2.31233	+	5.58246i	−0.149572	+	0.361100i	−0.980852	−	0.194755i	$-0.937609\pi$
$239$	−2.31233	+	5.58246i	−0.149572	+	0.361100i	0.831280	+	0.555854i	$0.187609\pi$
$240$	6.87339	−	12.0782i	0.443675	−	0.779646i
$241$	1.48411	+	3.58296i	0.0956000	+	0.230799i	0.964444	−	0.264287i	$-0.0851366\pi$
$241$	1.48411	+	3.58296i	0.0956000	+	0.230799i	−0.868844	+	0.495086i	$0.835137\pi$
$242$	5.42518	−	5.09712i	0.348744	−	0.327655i
$243$	−0.290285	−	0.956940i	−0.0186218	−	0.0613878i
$244$	6.50425	+	27.5074i	0.416392	+	1.76098i
$245$	−22.6422	+	2.23007i	−1.44656	+	0.142474i
$246$	15.3408	−	4.13617i	0.978093	−	0.263713i
$247$	0.0838038	−	0.421310i	0.00533231	−	0.0268073i
$248$	−0.768208	−	0.624467i	−0.0487813	−	0.0396537i
$249$	−11.8604	+	2.35918i	−0.751621	+	0.149507i
$250$	9.63802	+	3.25493i	0.609562	+	0.205860i
$251$	28.3456	+	8.59855i	1.78916	+	0.542736i	0.997656	−	0.0684292i	$-0.0217987\pi$
$251$	28.3456	+	8.59855i	1.78916	+	0.542736i	0.791503	+	0.611165i	$0.209299\pi$
$252$	−1.20689	−	0.590504i	−0.0760268	−	0.0371983i
$253$	9.26625	+	11.2910i	0.582564	+	0.709857i
$254$	−5.60458	+	3.49727i	−0.351663	+	0.219438i
$255$	−8.37006			−0.524154
$256$	−3.94821	+	15.5052i	−0.246763	+	0.969076i
$257$	−11.2020			−0.698759			−0.349380	−	0.936981i	$-0.613608\pi$
$257$	−11.2020			−0.698759			−0.349380	+	0.936981i	$0.613608\pi$
$258$	1.63231	−	1.01856i	0.101623	−	0.0634130i
$259$	3.80256	+	4.63343i	0.236279	+	0.287907i
$260$	1.98878	+	0.973067i	0.123339	+	0.0603471i
$261$	−1.66623	−	0.505446i	−0.103137	−	0.0312863i
$262$	24.7985	+	8.37490i	1.53206	+	0.517403i
$263$	28.5848	−	5.68587i	1.76261	−	0.350606i	0.795696	−	0.605696i	$-0.207105\pi$
$263$	28.5848	−	5.68587i	1.76261	−	0.350606i	0.966917	+	0.255091i	$0.0821053\pi$
$264$	−7.19496	+	8.85111i	−0.442819	+	0.544748i
$265$	−7.69562	+	38.6885i	−0.472738	+	2.37661i
$266$	1.23665	−	0.333425i	0.0758239	−	0.0204436i
$267$	5.52464	−	0.544130i	0.338103	−	0.0333002i
$268$	−0.363735	−	1.53829i	−0.0222187	−	0.0939661i
$269$	−7.39724	−	24.3854i	−0.451017	−	1.48681i	−0.828076	−	0.560616i	$-0.810564\pi$
$269$	−7.39724	−	24.3854i	−0.451017	−	1.48681i	0.377059	−	0.926189i	$-0.376936\pi$
$270$	−3.58083	+	3.36430i	−0.217923	+	0.204745i
$271$	9.38769	+	22.6639i	0.570262	+	1.37673i	0.901333	+	0.433128i	$0.142590\pi$
$271$	9.38769	+	22.6639i	0.570262	+	1.37673i	−0.331071	+	0.943606i	$0.607410\pi$
$272$	9.29259	−	2.55210i	0.563446	−	0.154744i
$273$	0.0819183	−	0.197768i	0.00495792	−	0.0119695i
$274$	−6.83035	−	18.0624i	−0.412637	−	1.09119i
$275$	−25.1470	−	13.4414i	−1.51642	−	0.810544i
$276$	−5.30238	−	4.93530i	−0.319166	−	0.297070i
$277$	0.729919	+	0.599029i	0.0438566	+	0.0359922i	0.656066	−	0.754703i	$-0.272219\pi$
$277$	0.729919	+	0.599029i	0.0438566	+	0.0359922i	−0.612210	+	0.790695i	$0.709719\pi$
$278$	3.98957	−	3.07119i	0.239278	−	0.184198i
$279$	0.194460	+	0.291030i	0.0116420	+	0.0174235i
$280$	0.0308484	+	6.60151i	0.00184354	+	0.394516i
$281$	12.5623	+	8.39387i	0.749405	+	0.500736i	0.870660	−	0.491885i	$-0.163692\pi$
$281$	12.5623	+	8.39387i	0.749405	+	0.500736i	−0.121255	+	0.992621i	$0.538692\pi$
$282$	7.09717	+	6.20452i	0.422631	+	0.369474i
$283$	−14.6011	+	7.80446i	−0.867947	+	0.463927i	−0.844349	−	0.535794i	$-0.820012\pi$
$283$	−14.6011	+	7.80446i	−0.867947	+	0.463927i	−0.0235983	+	0.999722i	$0.507512\pi$
$284$	11.8612	+	3.13862i	0.703830	+	0.186243i
$285$	0.459084	−	4.66116i	0.0271938	−	0.276103i
$286$	−1.47883	−	1.05623i	−0.0874448	−	0.0624561i
$287$	−5.33700	+	5.33700i	−0.315033	+	0.315033i
$288$	2.94970	−	4.82693i	0.173813	−	0.284430i
$289$	7.91671	+	7.91671i	0.465689	+	0.465689i
$290$	1.40674	+	8.43870i	0.0826067	+	0.495538i
$291$	9.26176	+	0.912204i	0.542934	+	0.0534743i
$292$	6.19573	−	8.12673i	0.362578	−	0.475581i
$293$	−8.48821	−	15.8803i	−0.495886	−	0.927738i	−0.998017	−	0.0629462i	$-0.979950\pi$
$293$	−8.48821	−	15.8803i	−0.495886	−	0.927738i	0.502131	−	0.864792i	$-0.332550\pi$
$294$	−9.24045	+	0.620108i	−0.538914	+	0.0361654i
$295$	20.8629	−	31.2236i	1.21469	−	1.81791i
$296$	−20.9172	+	14.1183i	−1.21579	+	0.820607i
$297$	3.35317	−	2.24052i	0.194571	−	0.130008i
$298$	15.1275	+	1.96760i	0.876311	+	0.113980i
$299$	0.732140	−	0.892115i	0.0423407	−	0.0515923i
$300$	13.2500	+	4.93988i	0.764989	+	0.285204i
$301$	−0.430849	+	0.806062i	−0.0248337	+	0.0464607i
$302$	−7.59760	−	3.42817i	−0.437193	−	0.197269i
$303$	10.5334	+	4.36310i	0.605131	+	0.250653i
$304$	0.911542	+	5.31488i	0.0522805	+	0.304829i
$305$	−45.3639	+	18.7904i	−2.59753	+	1.07593i
$306$	−3.40542	−	0.106172i	−0.194675	−	0.00606946i
$307$	−3.23394	+	0.981006i	−0.184571	+	0.0559889i	−0.381217	−	0.924486i	$-0.624495\pi$
$307$	−3.23394	+	0.981006i	−0.184571	+	0.0559889i	0.196646	+	0.980475i	$0.436995\pi$
$308$	0.865995	−	5.34888i	0.0493446	−	0.304781i
$309$	−1.23420	−	12.5310i	−0.0702111	−	0.712865i
$310$	0.857558	−	1.49069i	0.0487060	−	0.0846656i
$311$	14.1648	+	2.81756i	0.803213	+	0.159769i	0.579592	−	0.814907i	$-0.303212\pi$
$311$	14.1648	+	2.81756i	0.803213	+	0.159769i	0.223621	+	0.974676i	$0.428212\pi$
$312$	0.796807	+	0.421127i	0.0451103	+	0.0238416i
$313$	−0.252656	−	1.27019i	−0.0142810	−	0.0717953i	0.972988	−	0.230857i	$-0.0741530\pi$
$313$	−0.252656	−	1.27019i	−0.0142810	−	0.0717953i	−0.987269	+	0.159062i	$0.949153\pi$
$314$	−2.04131	−	4.12315i	−0.115198	−	0.232683i
$315$	0.677528	−	2.23351i	0.0381744	−	0.125844i
$316$	−2.06513	+	33.0869i	−0.116173	+	1.86128i
$317$	−17.3728	+	14.2575i	−0.975756	+	0.800782i	−0.979957	−	0.199209i	$-0.936163\pi$
$317$	−17.3728	+	14.2575i	−0.975756	+	0.800782i	0.00420105	+	0.999991i	$0.498663\pi$
$318$	−3.62177	+	15.6431i	−0.203099	+	0.877220i
$319$		−	7.02200i		−	0.393156i
$320$	−27.6845	−	2.46567i	−1.54761	−	0.137835i
$321$			15.9297i			0.889108i
$322$	3.35238	+	0.776163i	0.186821	+	0.0432539i
$323$	2.51062	−	2.06041i	0.139695	−	0.114644i
$324$	−1.49956	+	1.32337i	−0.0833091	+	0.0735205i
$325$	−0.653989	+	2.15591i	−0.0362768	+	0.119589i
$326$	7.66391	−	3.79427i	0.424465	−	0.210145i
$327$	2.61680	+	13.1555i	0.144709	+	0.727504i
$328$	−20.2738	−	24.4696i	−1.11943	−	1.35111i
$329$	−4.39206	−	0.873635i	−0.242142	−	0.0481651i
$330$	−17.1754	−	9.88058i	−0.945475	−	0.543908i
$331$	−0.107336	−	1.08980i	−0.00589973	−	0.0599010i	0.991784	−	0.127923i	$-0.0408311\pi$
$331$	−0.107336	−	1.08980i	−0.00589973	−	0.0599010i	−0.997684	+	0.0680223i	$0.978331\pi$
$332$	14.1487	+	19.6151i	0.776510	+	1.07652i
$333$	8.53808	−	2.59000i	0.467884	−	0.141931i
$334$	0.832659	−	26.7072i	0.0455611	−	1.46135i
$335$	2.53687	−	1.05081i	0.138604	−	0.0574118i
$336$	−0.0711877	+	2.68627i	−0.00388361	+	0.146548i
$337$	−22.6322	−	9.37457i	−1.23286	−	0.510665i	−0.331380	−	0.943497i	$-0.607514\pi$
$337$	−22.6322	−	9.37457i	−1.23286	−	0.510665i	−0.901475	+	0.432832i	$0.857514\pi$
$338$	7.50238	−	16.6269i	0.408076	−	0.904387i
$339$	5.96189	−	11.1539i	0.323805	−	0.605797i
$340$	6.95623	+	15.2264i	0.377255	+	0.825766i
$341$	−0.895487	+	1.09115i	−0.0484933	+	0.0590893i
$342$	0.245907	−	1.89060i	0.0132971	−	0.102232i
$343$	7.56807	−	5.05682i	0.408637	−	0.273043i
$344$	−3.20950	−	2.12289i	−0.173045	−	0.114459i
$345$	6.99096	−	10.4627i	0.376380	−	0.563293i
$346$	1.72151	+	25.6528i	0.0925489	+	1.37910i
$347$	9.85972	+	18.4462i	0.529297	+	0.990246i	0.994470	+	0.105026i	$0.0334925\pi$
$347$	9.85972	+	18.4462i	0.529297	+	0.990246i	−0.465172	+	0.885220i	$0.654008\pi$
$348$	0.465300	+	3.45119i	0.0249427	+	0.185003i
$349$	−19.9764	−	1.96750i	−1.06931	−	0.105318i	−0.451985	−	0.892026i	$-0.649284\pi$
$349$	−19.9764	−	1.96750i	−1.06931	−	0.105318i	−0.617326	+	0.786708i	$0.711784\pi$
$350$	−6.62600	+	1.10456i	−0.354175	+	0.0590413i
$351$	−0.225312	−	0.225312i	−0.0120263	−	0.0120263i
$352$	22.0811	+	5.73268i	1.17693	+	0.305553i
$353$	−1.74910	+	1.74910i	−0.0930950	+	0.0930950i	−0.752121	−	0.659026i	$-0.770969\pi$
$353$	−1.74910	+	1.74910i	−0.0930950	+	0.0930950i	0.659026	+	0.752121i	$0.270969\pi$
$354$	8.88431	−	12.4389i	0.472195	−	0.661121i
$355$	−2.08909	+	21.2109i	−0.110877	+	1.12576i
$356$	−5.58130	−	9.59792i	−0.295808	−	0.508689i
$357$	1.42738	−	0.762948i	0.0755448	−	0.0403795i
$358$	−6.41723	+	7.34048i	−0.339161	+	0.387956i
$359$	−19.4266	−	12.9804i	−1.02530	−	0.685082i	−0.0752428	−	0.997165i	$-0.523973\pi$
$359$	−19.4266	−	12.9804i	−1.02530	−	0.685082i	−0.950055	+	0.312083i	$0.898973\pi$
$360$	9.09614	+	3.71804i	0.479409	+	0.195958i
$361$	−9.54613	−	14.2868i	−0.502428	−	0.751936i
$362$	−2.76663	−	3.59394i	−0.145411	−	0.188893i
$363$	4.06890	+	3.33926i	0.213562	+	0.175266i
$364$	−0.427851	+	0.0153408i	−0.0224255	+	0.000804077i
$365$	15.6558	+	8.36821i	0.819463	+	0.438012i
$366$	−18.6950	+	7.06957i	−0.977204	+	0.369532i
$367$	6.03988	−	14.5816i	0.315279	−	0.761151i	−0.684213	−	0.729282i	$-0.739854\pi$
$367$	6.03988	−	14.5816i	0.315279	−	0.761151i	0.999492	−	0.0318690i	$-0.0101459\pi$
$368$	−4.57132	+	13.7475i	−0.238296	+	0.716637i
$369$	4.29942	+	10.3797i	0.223819	+	0.540347i
$370$	−30.0172	−	31.9492i	−1.56052	−	1.66096i
$371$	−2.21417	−	7.29915i	−0.114954	−	0.378953i
$372$	0.367813	−	0.595621i	0.0190702	−	0.0308815i
$373$	−14.5153	+	1.42964i	−0.751575	+	0.0740237i	−0.466548	−	0.884496i	$-0.654503\pi$
$373$	−14.5153	+	1.42964i	−0.751575	+	0.0740237i	−0.285027	+	0.958519i	$0.592003\pi$
$374$	−3.57688	−	13.2664i	−0.184956	−	0.685990i
$375$	−1.40334	+	7.05505i	−0.0724679	+	0.364321i
$376$	5.38859	−	18.0673i	0.277895	−	0.931750i
$377$	−0.544157	+	0.108240i	−0.0280255	+	0.00557462i
$378$	0.303989	−	0.900127i	0.0156355	−	0.0462975i
$379$	−7.73825	−	2.34737i	−0.397487	−	0.120576i	0.0852114	−	0.996363i	$-0.472843\pi$
$379$	−7.73825	−	2.34737i	−0.397487	−	0.120576i	−0.482699	+	0.875786i	$0.660343\pi$
$380$	−8.86087	+	3.03868i	−0.454553	+	0.155881i
$381$	−2.96345	−	3.61097i	−0.151822	−	0.184996i
$382$	0.199914	+	0.320373i	0.0102285	+	0.0163917i
$383$	−28.2949			−1.44580			−0.722900	−	0.690952i	$-0.757191\pi$
$383$	−28.2949			−1.44580			−0.722900	+	0.690952i	$0.757191\pi$
$384$	−11.2324	−	1.35435i	−0.573199	−	0.0691137i
$385$	9.41268			0.479714
$386$	2.51280	+	4.02692i	0.127898	+	0.204965i
$387$	0.863089	+	1.05168i	0.0438733	+	0.0534598i
$388$	−6.03788	−	17.6066i	−0.306527	−	0.893841i
$389$	−15.0482	−	4.56484i	−0.762977	−	0.231446i	−0.115268	−	0.993334i	$-0.536773\pi$
$389$	−15.0482	−	4.56484i	−0.762977	−	0.231446i	−0.647709	+	0.761888i	$0.724273\pi$
$390$	−0.500930	+	1.48328i	−0.0253656	+	0.0751088i
$391$	8.55809	−	1.70231i	0.432801	−	0.0860895i
$392$	8.80767	+	16.2944i	0.444854	+	0.822990i
$393$	−3.61077	+	18.1525i	−0.182139	+	0.915675i
$394$	0.296301	+	1.09896i	0.0149274	+	0.0553649i
$395$	−57.3107	+	5.64461i	−2.88361	+	0.284011i
$396$	−6.86261	−	4.23786i	−0.344859	−	0.212960i
$397$	6.68257	+	22.0295i	0.335389	+	1.10563i	0.948803	+	0.315868i	$0.102296\pi$
$397$	6.68257	+	22.0295i	0.335389	+	1.10563i	−0.613414	+	0.789761i	$0.710204\pi$
$398$	−6.12122	−	6.51519i	−0.306829	−	0.326577i
$399$	0.346585	+	0.836730i	0.0173509	+	0.0418889i
$400$	−2.02551	−	28.2092i	−0.101276	−	1.41046i
$401$	14.9652	−	36.1293i	0.747329	−	1.80421i	0.174268	−	0.984698i	$-0.444244\pi$
$401$	14.9652	−	36.1293i	0.747329	−	1.80421i	0.573061	−	0.819513i	$-0.305756\pi$
$402$	1.04548	−	0.395349i	0.0521436	−	0.0197182i
$403$	0.0983604	+	0.0525747i	0.00489968	+	0.00261893i
$404$	−0.817076	−	22.7880i	−0.0406510	−	1.13375i
$405$	−2.68564	−	2.20404i	−0.133450	−	0.109520i
$406$	−1.00910	−	1.31085i	−0.0500809	−	0.0650566i
$407$	19.9905	+	29.9179i	0.990893	+	1.48298i
$408$	2.63705	+	6.28320i	0.130554	+	0.311065i
$409$	19.9661	+	13.3409i	0.987259	+	0.659665i	0.940696	−	0.339250i	$-0.110173\pi$
$409$	19.9661	+	13.3409i	0.987259	+	0.659665i	0.0465624	+	0.998915i	$0.485173\pi$
$410$	36.3319	−	41.5590i	1.79430	−	2.05245i
$411$	12.0424	−	6.43681i	0.594009	−	0.317504i
$412$	−21.7701	+	12.6595i	−1.07253	+	0.623691i
$413$	−0.711735	+	7.22637i	−0.0350222	+	0.355586i
$414$	2.97704	−	4.16815i	0.146314	−	0.204853i
$415$	−29.7079	+	29.7079i	−1.45830	+	1.45830i
$416$	0.103877	−	1.79950i	0.00509301	−	0.0882278i
$417$	2.51738	+	2.51738i	0.123277	+	0.123277i
$418$	7.58405	−	1.26427i	0.370948	−	0.0618374i
$419$	−24.8135	−	2.44392i	−1.21222	−	0.119393i	−0.528369	−	0.849015i	$-0.677196\pi$
$419$	−24.8135	−	2.44392i	−1.21222	−	0.119393i	−0.683851	+	0.729622i	$0.739696\pi$
$420$	−4.62617	+	0.623714i	−0.225734	+	0.0304341i
$421$	3.76464	+	7.04316i	0.183478	+	0.343262i	0.956798	−	0.290753i	$-0.0939057\pi$
$421$	3.76464	+	7.04316i	0.183478	+	0.343262i	−0.773321	+	0.634015i	$0.781406\pi$
$422$	−2.70171	−	40.2591i	−0.131517	−	1.95978i
$423$	−3.70332	+	5.54242i	−0.180062	+	0.269482i
$424$	31.4671	−	6.41219i	1.52818	−	0.311404i
$425$	−14.1632	+	9.46352i	−0.687014	+	0.459048i
$426$	−1.11902	+	8.60330i	−0.0542165	+	0.416831i
$427$	6.02329	−	7.33940i	0.291488	−	0.355179i
$428$	28.9784	−	13.2389i	1.40073	−	0.639927i
$429$	0.605753	−	1.13328i	0.0292460	−	0.0547155i
$430$	2.74928	−	6.09303i	0.132582	−	0.293832i
$431$	17.7340	+	7.34565i	0.854215	+	0.353827i	0.766442	−	0.642313i	$-0.222025\pi$
$431$	17.7340	+	7.34565i	0.854215	+	0.353827i	0.0877726	+	0.996141i	$0.472025\pi$
$432$	3.65367	+	1.62810i	0.175787	+	0.0783318i
$433$	−21.4753	+	8.89534i	−1.03204	+	0.427483i	−0.833447	−	0.552600i	$-0.813636\pi$
$433$	−21.4753	+	8.89534i	−1.03204	+	0.427483i	−0.198589	+	0.980083i	$0.563636\pi$
$434$	−0.0103628	+	0.332381i	−0.000497429	+	0.0159548i
$435$	−5.78892	+	1.75605i	−0.277557	+	0.0841961i
$436$	21.7571	−	15.6937i	1.04198	−	0.751593i
$437$	0.478593	+	4.85924i	0.0228942	+	0.232449i
$438$	6.26354	+	3.60326i	0.299284	+	0.172170i
$439$	−2.05281	−	0.408329i	−0.0979751	−	0.0194885i	0.145859	−	0.989305i	$-0.453405\pi$
$439$	−2.05281	−	0.408329i	−0.0979751	−	0.0194885i	−0.243834	+	0.969817i	$0.578405\pi$
$440$	−3.70002	+	39.4562i	−0.176391	+	1.88100i
$441$	−1.27758	−	6.42285i	−0.0608374	−	0.305850i
$442$	−0.972922	+	0.481678i	−0.0462772	+	0.0229111i
$443$	2.39390	−	7.89165i	0.113738	−	0.374943i	−0.881528	−	0.472131i	$-0.843485\pi$
$443$	2.39390	−	7.89165i	0.113738	−	0.374943i	0.995266	+	0.0971880i	$0.0309848\pi$
$444$	−11.8075	−	13.3795i	−0.560357	−	0.634964i
$445$	14.9090	−	12.2355i	0.706753	−	0.580017i
$446$	11.0392	+	2.55585i	0.522720	+	0.121023i
$447$			10.7868i			0.510200i
$448$	4.94588	−	2.10302i	0.233671	−	0.0993582i
$449$			18.0510i			0.851879i	0.904752	+	0.425939i	$0.140056\pi$
$449$			18.0510i			0.851879i	−0.904752	+	0.425939i	$0.859944\pi$
$450$	−2.25539	+	9.74144i	−0.106320	+	0.459216i
$451$	−35.0240	+	28.7435i	−1.64922	+	1.35348i
$452$	−25.2454	−	1.57571i	−1.18745	−	0.0741150i
$453$	1.71091	−	5.64010i	0.0803853	−	0.264995i
$454$	−0.187283	−	0.378287i	−0.00878965	−	0.0177539i
$455$	−0.145090	−	0.729419i	−0.00680194	−	0.0341957i
$456$	−3.64366	+	1.12391i	−0.170630	+	0.0526319i
$457$	−35.0378	−	6.96945i	−1.63900	−	0.326017i	−0.712315	−	0.701860i	$-0.752353\pi$
$457$	−35.0378	−	6.96945i	−1.63900	−	0.326017i	−0.926683	+	0.375843i	$0.877353\pi$
$458$	−13.7827	+	23.9584i	−0.644022	+	1.11950i
$459$	−0.236140	−	2.39757i	−0.0110221	−	0.111909i
$460$	−24.8433	−	4.02218i	−1.15832	−	0.187535i
$461$	−2.23298	+	0.677368i	−0.104000	+	0.0315482i	−0.341856	−	0.939752i	$-0.611055\pi$
$461$	−2.23298	+	0.677368i	−0.104000	+	0.0315482i	0.237856	+	0.971301i	$0.423555\pi$
$462$	3.82962	+	0.119397i	0.178170	+	0.00555487i
$463$	7.96283	−	3.29831i	0.370064	−	0.153286i	−0.189898	−	0.981804i	$-0.560816\pi$
$463$	7.96283	−	3.29831i	0.370064	−	0.153286i	0.559962	+	0.828518i	$0.310816\pi$
$464$	5.89153	−	3.71469i	0.273507	−	0.172450i
$465$	1.12349	+	0.465363i	0.0521004	+	0.0215807i
$466$	−15.0354	−	6.78424i	−0.696501	−	0.314274i
$467$	−20.1553	+	37.7079i	−0.932675	+	1.74491i	−0.337474	+	0.941335i	$0.609572\pi$
$467$	−20.1553	+	37.7079i	−0.932675	+	1.74491i	−0.595201	+	0.803577i	$0.702928\pi$
$468$	−0.222622	+	0.597129i	−0.0102907	+	0.0276023i
$469$	−0.336839	+	0.410439i	−0.0155538	+	0.0189523i
$470$	32.4778	+	4.22433i	1.49809	+	0.194854i
$471$	2.70498	−	1.80741i	0.124639	−	0.0832811i
$472$	−30.0118	−	5.82407i	−1.38141	−	0.268074i
$473$	−3.04822	+	4.56198i	−0.140157	+	0.209760i
$474$	−23.3889	+	1.56958i	−1.07429	+	0.0720932i
$475$	−4.49326	−	8.40630i	−0.206165	−	0.385708i
$476$	−2.57419	−	1.96253i	−0.117988	−	0.0899525i
$477$	−11.2993	−	1.11288i	−0.517357	−	0.0509552i
$478$	1.40512	+	8.42895i	0.0642685	+	0.385531i
$479$	16.7640	+	16.7640i	0.765967	+	0.765967i	0.977394	−	0.211427i	$-0.0678111\pi$
$479$	16.7640	+	16.7640i	0.765967	+	0.765967i	−0.211427	+	0.977394i	$0.567811\pi$
$480$	−0.796000	−	19.6372i	−0.0363323	−	0.896313i
$481$	2.01030	−	2.01030i	0.0916616	−	0.0916616i
$482$	4.46308	+	3.18769i	0.203288	+	0.145195i
$483$	−0.238495	+	2.42148i	−0.0108519	+	0.110181i
$484$	2.69300	−	10.1771i	0.122409	−	0.462597i
$485$	28.5155	−	15.2419i	1.29482	−	0.692097i
$486$	−1.06471	−	0.930798i	−0.0482964	−	0.0422219i
$487$	−11.5774	−	7.73575i	−0.524621	−	0.350540i	0.264888	−	0.964279i	$-0.414665\pi$
$487$	−11.5774	−	7.73575i	−0.524621	−	0.350540i	−0.789509	+	0.613739i	$0.789665\pi$
$488$	28.3977	+	28.1336i	1.28551	+	1.27355i
$489$	3.35952	+	5.02788i	0.151923	+	0.227369i
$490$	−25.4963	+	19.6272i	−1.15181	+	0.886665i
$491$	9.68051	+	7.94459i	0.436875	+	0.358534i	0.826975	−	0.562238i	$-0.190060\pi$
$491$	9.68051	+	7.94459i	0.436875	+	0.358534i	−0.390100	+	0.920772i	$0.627560\pi$
$492$	15.3091	−	16.4477i	0.690186	−	0.741521i
$493$	−3.69954	−	1.97745i	−0.166619	−	0.0890597i
$494$	−0.214876	−	0.568224i	−0.00966771	−	0.0255656i
$495$	5.36181	−	12.9445i	0.240995	−	0.581814i
$496$	−1.38921	−	0.174094i	−0.0623772	−	0.00781706i
$497$	−1.57715	−	3.80759i	−0.0707451	−	0.170794i
$498$	−12.4637	+	11.7100i	−0.558512	+	0.524739i
$499$	0.152649	+	0.503216i	0.00683350	+	0.0225270i	0.960291	−	0.279001i	$-0.0900033\pi$
$499$	0.152649	+	0.503216i	0.00683350	+	0.0225270i	−0.953457	+	0.301528i	$0.902503\pi$
$500$	14.0005	−	3.31047i	0.626120	−	0.148049i
$501$	18.8030	−	1.85193i	0.840056	−	0.0827383i
$502$	40.4462	−	10.9051i	1.80520	−	0.486718i
$503$	2.19078	−	11.0138i	0.0976822	−	0.491081i	−0.900711	−	0.434418i	$-0.856954\pi$
$503$	2.19078	−	11.0138i	0.0976822	−	0.491081i	0.998393	−	0.0566630i	$-0.0180461\pi$
$504$	−1.89010	+	0.195081i	−0.0841919	+	0.00868960i
$505$	38.8500	−	7.72774i	1.72880	−	0.343880i
$506$	19.5708	+	6.60940i	0.870026	+	0.293824i
$507$	12.3431	+	3.74423i	0.548175	+	0.166287i
$508$	−4.10601	+	8.39197i	−0.182175	+	0.372334i
$509$	25.0384	+	30.5094i	1.10981	+	1.35230i	0.929555	+	0.368684i	$0.120191\pi$
$509$	25.0384	+	30.5094i	1.10981	+	1.35230i	0.180252	+	0.983620i	$0.442309\pi$
$510$	−10.0423	+	6.26642i	−0.444681	+	0.277482i
$511$	−3.43262			−0.151850
$512$	6.87128	+	21.5589i	0.303671	+	0.952777i
$513$	1.34812			0.0595209
$514$	−13.4400	+	8.38658i	−0.592812	+	0.369916i
$515$	−27.7526	−	33.8166i	−1.22292	−	1.49014i
$516$	1.19586	−	2.44412i	0.0526446	−	0.107596i
$517$	−25.7245	−	7.80345i	−1.13136	−	0.343195i
$518$	8.03117	+	2.71227i	0.352870	+	0.119170i
$519$	−17.8308	+	3.54676i	−0.782684	+	0.155685i
$520$	3.11462	−	0.321466i	0.136585	−	0.0140972i
$521$	−0.476524	+	2.39565i	−0.0208769	+	0.104955i	−0.989819	−	0.142333i	$-0.954540\pi$
$521$	−0.476524	+	2.39565i	−0.0208769	+	0.104955i	0.968942	+	0.247289i	$0.0795396\pi$
$522$	−2.37754	+	0.641031i	−0.104062	+	0.0280572i
$523$	−10.7245	+	1.05628i	−0.468952	+	0.0461877i	−0.329734	−	0.944074i	$-0.606959\pi$
$523$	−10.7245	+	1.05628i	−0.468952	+	0.0461877i	−0.139218	+	0.990262i	$0.544459\pi$
$524$	36.0230	−	8.51780i	1.57367	−	0.372102i
$525$	−1.37884	−	4.54541i	−0.0601773	−	0.198378i
$526$	30.0389	−	28.2224i	1.30976	−	1.23056i
$527$	0.322699	+	0.779064i	0.0140570	+	0.0339366i
$528$	−2.00587	+	16.0061i	−0.0872944	+	0.696577i
$529$	3.78163	−	9.12966i	0.164419	−	0.396942i
$530$	19.7318	+	52.1795i	0.857095	+	2.26653i
$531$	9.53245	+	5.09520i	0.413673	+	0.221113i
$532$	1.23409	−	1.32588i	0.0535047	−	0.0574843i
$533$	2.76730	+	2.27106i	0.119865	+	0.0983706i
$534$	6.22103	−	4.78898i	0.269210	−	0.207239i
$535$	30.7473	+	46.0167i	1.32932	+	1.98947i
$536$	−1.58808	−	1.57331i	−0.0685945	−	0.0679564i
$537$	−5.73242	−	3.83028i	−0.247372	−	0.165289i
$538$	−27.1318	−	23.7193i	−1.16973	−	1.02261i
$539$	23.2913	−	12.4495i	1.00323	−	0.536236i
$540$	−1.77749	+	6.71732i	−0.0764910	+	0.289067i
$541$	0.733760	−	7.44999i	0.0315468	−	0.320300i	−0.966441	−	0.256890i	$-0.917302\pi$
$541$	0.733760	−	7.44999i	0.0315468	−	0.320300i	0.997988	−	0.0634103i	$-0.0201977\pi$
$542$	28.2310	+	20.1636i	1.21263	+	0.866100i
$543$	2.26775	−	2.26775i	0.0973183	−	0.0973183i
$544$	9.23846	−	10.0191i	0.396096	−	0.429564i
$545$	32.9520	+	32.9520i	1.41151	+	1.41151i
$546$	−0.0497786	−	0.298610i	−0.00213033	−	0.0127793i
$547$	42.8813	+	4.22344i	1.83347	+	0.180581i	0.954880	−	0.296992i	$-0.0959836\pi$
$547$	42.8813	+	4.22344i	1.83347	+	0.180581i	0.878592	+	0.477574i	$0.158484\pi$
$548$	−21.7178	−	16.5574i	−0.927738	−	0.707297i
$549$	−6.66224	−	12.4642i	−0.284338	−	0.531958i
$550$	−40.2343	+	2.70004i	−1.71559	+	0.115130i
$551$	1.30412	−	1.95176i	0.0555575	−	0.0831476i
$552$	−10.0567	−	1.95159i	−0.428040	−	0.0830650i
$553$	9.25888	−	6.18658i	0.393728	−	0.263080i
$554$	1.32422	+	0.172239i	0.0562609	+	0.00731775i
$555$	19.6651	−	23.9620i	0.834736	−	1.01713i
$556$	2.48733	−	6.67165i	0.105486	−	0.282941i
$557$	−14.3017	+	26.7566i	−0.605983	+	1.13371i	0.372625	+	0.927982i	$0.378458\pi$
$557$	−14.3017	+	26.7566i	−0.605983	+	1.13371i	−0.978608	+	0.205733i	$0.934042\pi$
$558$	0.451196	+	0.203588i	0.0191006	+	0.00861856i
$559$	0.400509	+	0.165896i	0.0169397	+	0.00701666i
$560$	4.97937	+	7.89733i	0.210417	+	0.333723i
$561$	8.97619	−	3.71806i	0.378975	−	0.156977i
$562$	21.3564	+	0.665836i	0.900864	+	0.0280866i
$563$	26.0271	−	7.89523i	1.09691	−	0.332744i	0.310579	−	0.950548i	$-0.399477\pi$
$563$	26.0271	−	7.89523i	1.09691	−	0.332744i	0.786333	+	0.617803i	$0.211977\pi$
$564$	13.1603	+	2.13067i	0.554147	+	0.0897175i
$565$	−4.30686	−	43.7283i	−0.181191	−	1.83966i
$566$	−11.6753	+	20.2951i	−0.490749	+	0.853068i
$567$	0.658894	+	0.131062i	0.0276709	+	0.00550409i
$568$	16.5807	−	5.11442i	0.695710	−	0.214596i
$569$	−5.37951	−	27.0446i	−0.225521	−	1.13377i	−0.913124	−	0.407683i	$-0.866337\pi$
$569$	−5.37951	−	27.0446i	−0.225521	−	1.13377i	0.687603	−	0.726087i	$-0.258663\pi$
$570$	−2.93887	−	5.93611i	−0.123096	−	0.248636i
$571$	8.40404	−	27.7044i	0.351698	−	1.15939i	−0.585522	−	0.810656i	$-0.699111\pi$
$571$	8.40404	−	27.7044i	0.351698	−	1.15939i	0.937221	−	0.348737i	$-0.113389\pi$
$572$	−2.56504	−	0.160098i	−0.107250	−	0.00669405i
$573$	−0.206413	+	0.169399i	−0.00862303	+	0.00707673i
$574$	−2.40762	+	10.3989i	−0.100492	+	0.434043i
$575$		−	25.6084i		−	1.06794i
$576$	−0.0747652	−	7.99965i	−0.00311522	−	0.333319i
$577$		−	21.2637i		−	0.885221i	−0.896714	−	0.442610i	$-0.854052\pi$
$577$		−	21.2637i		−	0.885221i	0.896714	−	0.442610i	$-0.145948\pi$
$578$	15.4254	+	3.57137i	0.641611	+	0.148549i
$579$	−2.59450	+	2.12925i	−0.107824	+	0.0884886i
$580$	8.00560	+	9.07147i	0.332414	+	0.376672i
$581$	2.35825	−	7.77412i	0.0978369	−	0.322525i
$582$	11.7951	−	5.83955i	0.488922	−	0.242057i
$583$	−8.93288	−	44.9086i	−0.369962	−	1.85992i
$584$	1.34933	−	14.3889i	0.0558355	−	0.595418i
$585$	−1.08576	−	0.215972i	−0.0448908	−	0.00892933i
$586$	−22.0732	−	12.6982i	−0.911834	−	0.524556i
$587$	−2.90384	−	29.4832i	−0.119854	−	1.21690i	−0.847442	−	0.530887i	$-0.821859\pi$
$587$	−2.90384	−	29.4832i	−0.119854	−	1.21690i	0.727588	−	0.686014i	$-0.240641\pi$
$588$	−10.6223	+	7.66205i	−0.438058	+	0.315978i
$589$	−0.451548	+	0.136976i	−0.0186057	+	0.00564398i
$590$	1.65493	−	53.0812i	0.0681325	−	2.18532i
$591$	−0.743568	+	0.307996i	−0.0305863	+	0.0126693i
$592$	−14.5263	+	32.5990i	−0.597028	+	1.33981i
$593$	−39.3791	−	16.3114i	−1.61711	−	0.669827i	−0.623406	−	0.781898i	$-0.714252\pi$
$593$	−39.3791	−	16.3114i	−1.61711	−	0.669827i	−0.993700	+	0.112071i	$0.964252\pi$
$594$	2.34569	−	5.19857i	0.0962448	−	0.213300i
$595$	2.65068	−	4.95907i	0.108667	−	0.203302i
$596$	19.6229	−	8.96479i	0.803784	−	0.367212i
$597$	4.01017	−	4.88641i	0.164125	−	0.199987i
$598$	0.210513	−	1.61848i	0.00860851	−	0.0661846i
$599$	−28.8343	+	19.2665i	−1.17814	+	0.787207i	−0.981159	−	0.193200i	$-0.938113\pi$
$599$	−28.8343	+	19.2665i	−1.17814	+	0.787207i	−0.196980	+	0.980408i	$0.563113\pi$
$600$	19.5955	−	3.99308i	0.799985	−	0.163017i
$601$	7.08052	−	10.5967i	0.288820	−	0.432250i	−0.658479	−	0.752599i	$-0.728800\pi$
$601$	7.08052	−	10.5967i	0.288820	−	0.432250i	0.947300	+	0.320349i	$0.103800\pi$
$602$	0.0865470	+	1.28967i	0.00352739	+	0.0525630i
$603$	0.372571	+	0.697030i	0.0151722	+	0.0283853i
$604$	−11.6821	+	1.57501i	−0.475337	+	0.0640864i
$605$	18.1994	+	1.79248i	0.739911	+	0.0728748i
$606$	15.9044	−	2.65129i	0.646073	−	0.107701i
$607$	3.63163	+	3.63163i	0.147403	+	0.147403i	0.776957	−	0.629554i	$-0.216762\pi$
$607$	3.63163	+	3.63163i	0.147403	+	0.147403i	−0.629554	+	0.776957i	$0.716762\pi$
$608$	5.07275	+	5.69428i	0.205727	+	0.230934i
$609$	0.827137	−	0.827137i	0.0335173	−	0.0335173i
$610$	−40.3594	+	56.5071i	−1.63410	+	2.28791i
$611$	−0.208187	+	2.11376i	−0.00842236	+	0.0855137i
$612$	−4.16527	+	2.42215i	−0.168371	+	0.0979098i
$613$	1.19342	−	0.637898i	0.0482019	−	0.0257644i	−0.447120	−	0.894474i	$-0.647550\pi$
$613$	1.19342	−	0.637898i	0.0482019	−	0.0257644i	0.495322	+	0.868710i	$0.335050\pi$
$614$	−3.14560	+	3.59816i	−0.126946	+	0.145210i
$615$	32.4548	+	21.6856i	1.30870	+	0.874447i
$616$	−2.96554	−	7.06587i	−0.119485	−	0.284692i
$617$	7.20017	+	10.7758i	0.289868	+	0.433818i	0.947612	−	0.319423i	$-0.103489\pi$
$617$	7.20017	+	10.7758i	0.289868	+	0.433818i	−0.657744	+	0.753241i	$0.728489\pi$
$618$	−10.8624	−	14.1106i	−0.436949	−	0.567610i
$619$	−26.2400	−	21.5346i	−1.05467	−	0.865548i	−0.0634817	−	0.997983i	$-0.520220\pi$
$619$	−26.2400	−	21.5346i	−1.05467	−	0.865548i	−0.991192	+	0.132435i	$0.957720\pi$
$620$	−0.0871485	−	2.43054i	−0.00349997	−	0.0976130i
$621$	3.19423	+	1.70735i	0.128180	+	0.0685136i
$622$	19.1042	−	7.22431i	0.766009	−	0.289668i
$623$	−1.42719	+	3.44554i	−0.0571791	+	0.138043i
$624$	1.27128	−	0.0912826i	0.0508921	−	0.00365423i
$625$	−3.96499	−	9.57233i	−0.158599	−	0.382893i
$626$	−1.25409	−	1.33480i	−0.0501234	−	0.0533494i
$627$	1.57820	+	5.20263i	0.0630273	+	0.207773i
$628$	−5.53602	−	3.41865i	−0.220911	−	0.136419i
$629$	21.3917	−	2.10690i	0.852944	−	0.0840077i
$630$	−0.859273	−	3.18699i	−0.0342343	−	0.126973i
$631$	4.41602	−	22.2008i	0.175799	−	0.883801i	−0.787694	−	0.616067i	$-0.788725\pi$
$631$	4.41602	−	22.2008i	0.175799	−	0.883801i	0.963493	−	0.267734i	$-0.0862748\pi$
$632$	22.2935	+	41.2434i	0.886786	+	1.64057i
$633$	27.9833	−	5.56622i	1.11224	−	0.221238i
$634$	−10.1696	+	30.1125i	−0.403884	+	1.19592i
$635$	−15.5305	−	4.71112i	−0.616309	−	0.186955i
$636$	7.36615	+	21.4799i	0.292087	+	0.851734i
$637$	−1.32377	−	1.61302i	−0.0524496	−	0.0639100i
$638$	−5.25716	−	8.42491i	−0.208133	−	0.333546i
$639$	−6.13470			−0.242685
$640$	−35.0615	+	17.7683i	−1.38593	+	0.702352i
$641$	42.9829			1.69772			0.848862	−	0.528615i	$-0.177288\pi$
$641$	42.9829			1.69772			0.848862	+	0.528615i	$0.177288\pi$
$642$	11.9261	+	19.1122i	0.470685	+	0.754300i
$643$	−3.52568	−	4.29606i	−0.139039	−	0.169420i	0.698835	−	0.715283i	$-0.253702\pi$
$643$	−3.52568	−	4.29606i	−0.139039	−	0.169420i	−0.837875	+	0.545863i	$0.816202\pi$
$644$	4.60324	−	1.57860i	0.181393	−	0.0622056i
$645$	4.52318	+	1.37209i	0.178100	+	0.0540260i
$646$	1.46964	−	4.35168i	0.0578223	−	0.171215i
$647$	−38.7541	+	7.70868i	−1.52358	+	0.303059i	−0.884669	−	0.466220i	$-0.845616\pi$
$647$	−38.7541	+	7.70868i	−1.52358	+	0.303059i	−0.638913	+	0.769279i	$0.720616\pi$
$648$	−0.808392	+	2.71044i	−0.0317566	+	0.106476i
$649$	−8.50394	+	42.7522i	−0.333809	+	1.67817i
$650$	0.829420	+	3.07626i	0.0325325	+	0.120661i
$651$	−0.234011	+	0.0230481i	−0.00917161	+	0.000903325i
$652$	6.35441	−	10.2901i	0.248858	−	0.402990i
$653$	−3.46406	−	11.4195i	−0.135559	−	0.446879i	0.862709	−	0.505700i	$-0.168766\pi$
$653$	−3.46406	−	11.4195i	−0.135559	−	0.446879i	−0.998269	+	0.0588212i	$0.981266\pi$
$654$	12.9888	+	13.8248i	0.507901	+	0.540591i
$655$	24.6074	+	59.4074i	0.961489	+	2.32124i
$656$	−42.6440	−	14.1800i	−1.66497	−	0.553636i
$657$	−1.95535	+	4.72063i	−0.0762854	+	0.184169i
$658$	−5.92361	+	2.24003i	−0.230926	+	0.0873254i
$659$	−13.8185	−	7.38612i	−0.538291	−	0.287722i	0.179763	−	0.983710i	$-0.442467\pi$
$659$	−13.8185	−	7.38612i	−0.538291	−	0.287722i	−0.718054	+	0.695988i	$0.754967\pi$
$660$	−28.0042	+	1.00410i	−1.09006	+	0.0390847i
$661$	18.2235	+	14.9556i	0.708810	+	0.581706i	0.918195	−	0.396128i	$-0.129646\pi$
$661$	18.2235	+	14.9556i	0.708810	+	0.581706i	−0.209385	+	0.977833i	$0.567146\pi$
$662$	−0.944684	−	1.22717i	−0.0367162	−	0.0476954i
$663$	−0.426487	−	0.638282i	−0.0165634	−	0.0247888i
$664$	31.6607	+	12.9413i	1.22867	+	0.502219i
$665$	2.61624	+	1.74812i	0.101454	+	0.0677891i
$666$	8.30484	−	9.49966i	0.321806	−	0.368104i
$667$	5.56182	−	2.97285i	0.215354	−	0.115109i
$668$	−18.9958	−	32.6663i	−0.734971	−	1.26390i
$669$	−0.785348	+	7.97377i	−0.0303633	+	0.308284i
$670$	2.25700	−	3.16003i	0.0871957	−	0.122083i
$671$	40.3022	−	40.3022i	1.55585	−	1.55585i
$672$	1.92572	+	3.27625i	0.0742862	+	0.126384i
$673$	−24.6112	−	24.6112i	−0.948694	−	0.948694i	0.0500527	−	0.998747i	$-0.484061\pi$
$673$	−24.6112	−	24.6112i	−0.948694	−	0.948694i	−0.998747	+	0.0500527i	$0.984061\pi$
$674$	−34.1723	+	5.69657i	−1.31627	+	0.219424i
$675$	−7.03640	−	0.693025i	−0.270831	−	0.0266745i
$676$	−3.44684	−	25.5656i	−0.132571	−	0.983293i
$677$	−1.71487	−	3.20829i	−0.0659077	−	0.123305i	0.846810	−	0.531896i	$-0.178520\pi$
$677$	−1.71487	−	3.20829i	−0.0659077	−	0.123305i	−0.912717	+	0.408591i	$0.866020\pi$
$678$	−1.19760	−	17.8458i	−0.0459934	−	0.685365i
$679$	−3.47352	+	5.19850i	−0.133302	+	0.199500i
$680$	19.7455	+	13.0605i	0.757207	+	0.500847i
$681$	0.248174	−	0.165824i	0.00951004	−	0.00635441i
$682$	−0.257480	+	1.97958i	−0.00985942	+	0.0758020i
$683$	−23.7260	+	28.9102i	−0.907851	+	1.10622i	0.0860882	+	0.996288i	$0.472563\pi$
$683$	−23.7260	+	28.9102i	−0.907851	+	1.10622i	−0.993939	+	0.109932i	$0.964937\pi$
$684$	−1.12040	−	2.45243i	−0.0428396	−	0.0937709i
$685$	22.3631	−	41.8384i	0.854451	−	1.59856i
$686$	5.29419	−	11.7331i	0.202133	−	0.447972i
$687$	−18.0567	−	7.47932i	−0.688905	−	0.285354i
$688$	−5.44007	−	0.144165i	−0.207401	−	0.00549625i
$689$	−3.34242	+	1.38448i	−0.127336	+	0.0527443i
$690$	0.554551	−	17.7870i	0.0211114	−	0.677138i
$691$	36.5230	−	11.0791i	1.38940	−	0.421470i	0.495060	−	0.868859i	$-0.335146\pi$
$691$	36.5230	−	11.0791i	1.38940	−	0.421470i	0.894340	+	0.447389i	$0.147646\pi$
$692$	21.2710	+	29.4891i	0.808601	+	1.12101i
$693$	0.265554	+	2.69622i	0.0100876	+	0.102421i
$694$	25.6397	+	14.7499i	0.973271	+	0.559899i
$695$	12.1311	+	2.41302i	0.460158	+	0.0915312i
$696$	3.14207	+	3.79235i	0.119100	+	0.143748i
$697$	5.28048	+	26.5468i	0.200012	+	1.00553i
$698$	−25.4404	+	12.5951i	−0.962934	+	0.476733i
$699$	3.38583	−	11.1616i	0.128064	−	0.422169i
$700$	−7.12285	+	6.28593i	−0.269218	+	0.237586i
$701$	−22.3069	+	18.3068i	−0.842521	+	0.691440i	−0.953175	−	0.302420i	$-0.902206\pi$
$701$	−22.3069	+	18.3068i	−0.842521	+	0.691440i	0.110653	+	0.993859i	$0.464706\pi$
$702$	−0.439011	−	0.101642i	−0.0165694	−	0.00383624i
$703$			12.0283i			0.453655i
$704$	30.7845	−	9.65347i	1.16024	−	0.363829i
$705$			23.1587i			0.872208i
$706$	−0.789049	+	3.40804i	−0.0296963	+	0.128263i
$707$	−5.92082	+	4.85909i	−0.222676	+	0.182745i
$708$	1.34664	−	21.5755i	0.0506099	−	0.810856i
$709$	1.78445	−	5.88253i	0.0670162	−	0.220923i	−0.917035	−	0.398806i	$-0.869425\pi$
$709$	1.78445	−	5.88253i	0.0670162	−	0.220923i	0.984052	+	0.177883i	$0.0569248\pi$
$710$	13.3735	+	27.0126i	0.501898	+	1.01376i
$711$	−3.23375	−	16.2571i	−0.121275	−	0.609691i
$712$	−13.8821	−	7.33692i	−0.520252	−	0.274963i
$713$	−1.24337	−	0.247322i	−0.0465646	−	0.00926227i
$714$	1.14135	−	1.98401i	0.0427140	−	0.0742497i
$715$	−0.437596	−	4.44298i	−0.0163651	−	0.166158i
$716$	−2.20372	+	13.6114i	−0.0823568	+	0.508682i
$717$	−5.78223	+	1.75402i	−0.215941	+	0.0655051i
$718$	−33.0259	−	1.02966i	−1.23252	−	0.0384266i
$719$	42.9973	−	17.8101i	1.60353	−	0.664203i	0.611618	−	0.791153i	$-0.290519\pi$
$719$	42.9973	−	17.8101i	1.60353	−	0.664203i	0.991909	+	0.126950i	$0.0405188\pi$
$720$	13.6970	−	2.34915i	0.510458	−	0.0875475i
$721$	7.81519	+	3.23716i	0.291053	+	0.120558i
$722$	−22.1494	−	9.99422i	−0.824316	−	0.371946i
$723$	−1.82816	+	3.42024i	−0.0679899	+	0.127200i
$724$	−6.01006	−	2.24067i	−0.223362	−	0.0832740i
$725$	−7.81010	+	9.51663i	−0.290060	+	0.353439i
$726$	7.38182	+	0.960140i	0.273965	+	0.0356342i
$727$	0.466433	−	0.311660i	0.0172990	−	0.0115588i	−0.546891	−	0.837204i	$-0.684189\pi$
$727$	0.466433	−	0.311660i	0.0172990	−	0.0115588i	0.564190	+	0.825645i	$0.309189\pi$
$728$	−0.501845	+	0.338725i	−0.0185996	+	0.0125540i
$729$	0.555570	−	0.831470i	0.0205767	−	0.0307952i
$730$	25.0487	−	1.68097i	0.927094	−	0.0622154i
$731$	1.54508	+	2.89064i	0.0571468	+	0.106914i
$732$	−17.1373	+	22.4784i	−0.633412	+	0.830825i
$733$	−30.6165	−	3.01547i	−1.13085	−	0.111379i	−0.484764	−	0.874645i	$-0.661094\pi$
$733$	−30.6165	−	3.01547i	−1.13085	−	0.111379i	−0.646084	+	0.763266i	$0.723594\pi$
$734$	−3.67020	−	22.0167i	−0.135470	−	0.812650i
$735$	−16.0879	−	16.0879i	−0.593413	−	0.593413i
$736$	4.80772	+	19.9165i	0.177215	+	0.734131i
$737$	−2.25381	+	2.25381i	−0.0830200	+	0.0830200i
$738$	12.9294	+	9.23463i	0.475938	+	0.339931i
$739$	−4.47438	+	45.4292i	−0.164593	+	1.67114i	0.458274	+	0.888811i	$0.348468\pi$
$739$	−4.47438	+	45.4292i	−0.164593	+	1.67114i	−0.622867	+	0.782328i	$0.714032\pi$
$740$	−59.9337	−	15.8592i	−2.20321	−	0.582997i
$741$	0.378842	−	0.202495i	0.0139171	−	0.00743884i
$742$	−8.12120	−	7.09975i	−0.298139	−	0.260640i
$743$	−21.2275	−	14.1838i	−0.778761	−	0.520351i	0.101503	−	0.994835i	$-0.467635\pi$
$743$	−21.2275	−	14.1838i	−0.778761	−	0.520351i	−0.880264	+	0.474484i	$0.842635\pi$
$744$	−0.00462615	−	0.989991i	−0.000169603	−	0.0362948i
$745$	20.8207	+	31.1604i	0.762811	+	1.14163i
$746$	−16.3450	+	12.5825i	−0.598433	+	0.460677i
$747$	−9.34782	−	7.67156i	−0.342019	−	0.280688i
$748$	−14.2237	−	13.2390i	−0.520069	−	0.484065i
$749$	−9.43797	−	5.04470i	−0.344856	−	0.184329i
$750$	3.59820	+	9.51520i	0.131388	+	0.347446i
$751$	7.96778	−	19.2359i	0.290749	−	0.701929i	−0.709247	−	0.704960i	$-0.750965\pi$
$751$	7.96778	−	19.2359i	0.290749	−	0.701929i	0.999995	+	0.00303104i	$0.000964813\pi$
$752$	−7.06128	−	25.7112i	−0.257499	−	0.937591i
$753$	11.3355	+	27.3663i	0.413089	+	0.997284i
$754$	−0.571838	+	0.537259i	−0.0208251	+	0.0195658i
$755$	−5.94412	−	19.5951i	−0.216329	−	0.713140i
$756$	−0.309176	−	1.30755i	−0.0112446	−	0.0475551i
$757$	16.8458	−	1.65917i	0.612272	−	0.0603035i	0.212872	−	0.977080i	$-0.431718\pi$
$757$	16.8458	−	1.65917i	0.612272	−	0.0603035i	0.399400	+	0.916777i	$0.369218\pi$
$758$	−11.0417	+	2.97705i	−0.401052	+	0.108131i
$759$	−2.84958	+	14.3258i	−0.103433	+	0.519994i
$760$	−8.35620	+	10.2796i	−0.303111	+	0.372882i
$761$	−16.4293	+	3.26798i	−0.595560	+	0.118464i	−0.483661	−	0.875255i	$-0.660693\pi$
$761$	−16.4293	+	3.26798i	−0.595560	+	0.118464i	−0.111899	+	0.993720i	$0.535693\pi$
$762$	−6.25894	−	2.11376i	−0.226737	−	0.0765733i
$763$	−8.62306	−	2.61578i	−0.312176	−	0.0946975i
$764$	0.479708	+	0.234711i	0.0173552	+	0.00849154i
$765$	−5.30991	−	6.47014i	−0.191980	−	0.233929i
$766$	−33.9479	+	21.1835i	−1.22659	+	0.765392i
$767$	3.44409			0.124359
$768$	−14.4904	+	6.78440i	−0.522878	+	0.244811i
$769$	−5.74035			−0.207002			−0.103501	−	0.994629i	$-0.533005\pi$
$769$	−5.74035			−0.207002			−0.103501	+	0.994629i	$0.533005\pi$
$770$	11.2932	−	7.04699i	0.406979	−	0.253956i
$771$	−7.10645	−	8.65924i	−0.255933	−	0.311855i
$772$	6.02967	+	2.95019i	0.217013	+	0.106180i
$773$	−22.8610	−	6.93480i	−0.822252	−	0.249427i	−0.148997	−	0.988838i	$-0.547604\pi$
$773$	−22.8610	−	6.93480i	−0.822252	−	0.249427i	−0.673255	+	0.739410i	$0.735104\pi$
$774$	1.82288	+	0.615621i	0.0655222	+	0.0221280i
$775$	2.42723	−	0.482807i	0.0871888	−	0.0173429i
$776$	−20.4257	−	16.6038i	−0.733241	−	0.596043i
$777$	−1.16937	+	5.87883i	−0.0419510	+	0.210902i
$778$	−21.4723	+	5.78934i	−0.769818	+	0.207558i
$779$	−15.0731	+	1.48457i	−0.540050	+	0.0531903i
$780$	0.509477	+	2.15465i	0.0182422	+	0.0771490i
$781$	−7.18169	−	23.6749i	−0.256981	−	0.847154i
$782$	8.99343	−	8.44960i	0.321604	−	0.302157i
$783$	−0.666332	−	1.60867i	−0.0238128	−	0.0574891i
$784$	22.7665	+	12.9558i	0.813088	+	0.462706i
$785$	4.32533	−	10.4423i	0.154378	−	0.372701i
$786$	9.25812	+	24.4825i	0.330226	+	0.873261i
$787$	−36.6219	−	19.5748i	−1.30543	−	0.697766i	−0.335704	−	0.941968i	$-0.608974\pi$
$787$	−36.6219	−	19.5748i	−1.30543	−	0.697766i	−0.969724	+	0.244202i	$0.921474\pi$
$788$	1.17826	+	1.09669i	0.0419737	+	0.0390679i
$789$	22.5292	+	18.4893i	0.802062	+	0.658235i
$790$	−64.5348	+	49.6792i	−2.29604	+	1.76751i
$791$	4.72039	+	7.06456i	0.167838	+	0.251187i
$792$	−11.4064	+	0.0533014i	−0.405310	+	0.00189398i
$793$	−3.74438	−	2.50191i	−0.132967	−	0.0888456i
$794$	24.5105	+	21.4277i	0.869845	+	0.760440i
$795$	−34.7886	+	18.5949i	−1.23383	+	0.659494i
$796$	−12.2219	−	3.23407i	−0.433194	−	0.114629i
$797$	−0.291927	+	2.96398i	−0.0103406	+	0.104990i	−0.998970	−	0.0453859i	$-0.985548\pi$
$797$	−0.291927	+	2.96398i	−0.0103406	+	0.104990i	0.988629	+	0.150375i	$0.0480483\pi$
$798$	1.04226	+	0.744421i	0.0368957	+	0.0263522i
$799$	−11.3555	+	11.3555i	−0.401727	+	0.401727i
$800$	−23.5496	−	32.3286i	−0.832603	−	1.14299i
$801$	3.92541	+	3.92541i	0.138698	+	0.138698i
$802$	−9.09381	−	54.5516i	−0.321114	−	1.92628i
$803$	−20.5068	−	2.01974i	−0.723669	−	0.0712752i
$804$	0.958363	−	1.25705i	0.0337989	−	0.0443328i
$805$	3.98498	+	7.45537i	0.140452	+	0.262767i
$806$	0.157373	−	0.0105610i	0.00554322	−	0.000371994i
$807$	14.1574	−	21.1881i	0.498365	−	0.745856i
$808$	−18.0410	−	26.7291i	−0.634681	−	0.940325i
$809$	−22.9675	+	15.3464i	−0.807493	+	0.539549i	−0.889421	−	0.457089i	$-0.848892\pi$
$809$	−22.9675	+	15.3464i	−0.807493	+	0.539549i	0.0819283	+	0.996638i	$0.473892\pi$
$810$	−4.87230	−	0.633731i	−0.171195	−	0.0222670i
$811$	−19.4780	+	23.7340i	−0.683964	+	0.833412i	−0.993059	−	0.117619i	$-0.962474\pi$
$811$	−19.4780	+	23.7340i	−0.683964	+	0.833412i	0.309095	+	0.951031i	$0.399974\pi$
$812$	−2.19211	−	0.817263i	−0.0769279	−	0.0286803i
$813$	−11.5639	+	21.6346i	−0.405565	+	0.758759i
$814$	46.3831	+	20.9289i	1.62573	+	0.733557i
$815$	19.4096	+	8.03971i	0.679888	+	0.281619i
$816$	7.86796	+	5.56423i	0.275434	+	0.194787i
$817$	−1.69450	+	0.701884i	−0.0592830	+	0.0245558i
$818$	33.9430	+	1.05825i	1.18679	+	0.0370010i
$819$	0.204845	−	0.0621391i	0.00715787	−	0.00217132i
$820$	12.4766	−	77.0626i	0.435702	−	2.69114i
$821$	0.0861831	+	0.875031i	0.00300781	+	0.0305388i	0.996571	−	0.0827362i	$-0.0263659\pi$
$821$	0.0861831	+	0.875031i	0.00300781	+	0.0305388i	−0.993564	+	0.113275i	$0.963866\pi$
$822$	9.62931	−	16.7386i	0.335861	−	0.583826i
$823$	−7.87918	−	1.56727i	−0.274651	−	0.0546315i	0.0558431	−	0.998440i	$-0.482215\pi$
$823$	−7.87918	−	1.56727i	−0.274651	−	0.0546315i	−0.330494	+	0.943808i	$0.607215\pi$
$824$	−16.6416	+	31.4874i	−0.579739	+	1.09691i
$825$	−5.56279	−	27.9660i	−0.193671	−	0.973652i
$826$	4.55624	+	9.20297i	0.158532	+	0.320212i
$827$	−3.96394	+	13.0673i	−0.137840	+	0.454396i	−0.998498	−	0.0547864i	$-0.982552\pi$
$827$	−3.96394	+	13.0673i	−0.137840	+	0.454396i	0.860659	+	0.509183i	$0.170052\pi$
$828$	0.451246	−	7.22972i	0.0156819	−	0.251250i
$829$	39.5154	−	32.4295i	1.37243	−	1.12632i	0.394145	−	0.919048i	$-0.371041\pi$
$829$	39.5154	−	32.4295i	1.37243	−	1.12632i	0.978283	−	0.207274i	$-0.0664592\pi$
$830$	−13.4018	+	57.8846i	−0.465182	+	2.00920i
$831$			0.944255i			0.0327558i
$832$	−1.22260	−	2.23679i	−0.0423861	−	0.0775468i
$833$		−	15.7769i		−	0.546636i
$834$	4.90502	+	1.13564i	0.169847	+	0.0393239i
$835$	50.7424	−	41.6432i	1.75601	−	1.44112i
$836$	8.15273	−	7.19481i	0.281968	−	0.248838i
$837$	−0.101605	+	0.334947i	−0.00351198	+	0.0115775i
$838$	−31.6007	+	15.6450i	−1.09163	+	0.540446i
$839$	2.38112	+	11.9707i	0.0822055	+	0.413275i	0.999873	+	0.0159261i	$0.00506966\pi$
$839$	2.38112	+	11.9707i	0.0822055	+	0.413275i	−0.917668	+	0.397349i	$0.869930\pi$
$840$	−5.08347	+	4.21180i	−0.175396	+	0.145321i
$841$	25.4692	+	5.06614i	0.878249	+	0.174695i
$842$	9.78978	+	5.63182i	0.337378	+	0.194085i
$843$	1.48090	+	15.0358i	0.0510049	+	0.517861i
$844$	−33.3823	−	46.2797i	−1.14907	−	1.59301i
$845$	42.8830	−	13.0084i	1.47522	−	0.447503i
$846$	−0.293763	+	9.42230i	−0.0100998	+	0.323945i
$847$	−3.26700	+	1.35323i	−0.112255	+	0.0464977i
$848$	32.9532	−	31.2517i	1.13162	−	1.07319i
$849$	−15.2958	−	6.33572i	−0.524950	−	0.217441i
$850$	−9.90774	+	21.9578i	−0.339833	+	0.753145i
$851$	−15.2334	+	28.4998i	−0.522195	+	0.976959i
$852$	5.09846	+	11.1599i	0.174670	+	0.382332i
$853$	−9.86023	+	12.0147i	−0.337608	+	0.411376i	−0.913947	−	0.405835i	$-0.866981\pi$
$853$	−9.86023	+	12.0147i	−0.337608	+	0.411376i	0.576339	+	0.817211i	$0.304481\pi$
$854$	1.73188	−	13.3152i	0.0592638	−	0.455637i
$855$	3.89436	−	2.60213i	0.133184	−	0.0889910i
$856$	24.8564	−	37.5792i	0.849574	−	1.28443i
$857$	−10.5645	+	15.8109i	−0.360876	+	0.540089i	−0.966833	−	0.255408i	$-0.917790\pi$
$857$	−10.5645	+	15.8109i	−0.360876	+	0.540089i	0.605958	+	0.795497i	$0.292790\pi$
$858$	−0.121681	−	1.81321i	−0.00415412	−	0.0619020i
$859$	−6.72532	−	12.5822i	−0.229465	−	0.429299i	0.740668	−	0.671871i	$-0.234509\pi$
$859$	−6.72532	−	12.5822i	−0.229465	−	0.429299i	−0.970133	+	0.242572i	$0.922009\pi$
$860$	−1.26311	−	9.36865i	−0.0430717	−	0.319468i
$861$	−7.51132	−	0.739800i	−0.255985	−	0.0252123i
$862$	26.7765	−	4.46367i	0.912010	−	0.152033i
$863$	−3.83562	−	3.83562i	−0.130566	−	0.130566i	0.638804	−	0.769370i	$-0.279430\pi$
$863$	−3.83562	−	3.83562i	−0.130566	−	0.130566i	−0.769370	+	0.638804i	$0.779430\pi$
$864$	5.60254	−	0.782024i	0.190602	−	0.0266050i
$865$	−44.6625	+	44.6625i	−1.51857	+	1.51857i
$866$	−19.1061	+	26.7504i	−0.649251	+	0.909016i
$867$	−1.09739	+	11.1420i	−0.0372694	+	0.378402i
$868$	0.236411	+	0.406546i	0.00802431	+	0.0137991i
$869$	58.9535	−	31.5113i	1.99986	−	1.06895i
$870$	−5.63078	+	6.44088i	−0.190901	+	0.218366i
$871$	0.209396	+	0.139914i	0.00709510	+	0.00474080i
$872$	14.3545	−	35.1181i	0.486104	−	1.18925i
$873$	5.17045	+	7.73813i	0.174993	+	0.261896i
$874$	4.21218	+	5.47175i	0.142479	+	0.185085i
$875$	−3.73554	−	3.06567i	−0.126284	−	0.103639i
$876$	10.2126	−	0.366177i	0.345051	−	0.0123720i
$877$	29.8929	+	15.9781i	1.00941	+	0.539541i	0.891278	−	0.453456i	$-0.149809\pi$
$877$	29.8929	+	15.9781i	1.00941	+	0.539541i	0.118132	+	0.992998i	$0.462309\pi$
$878$	−2.76864	+	1.04697i	−0.0934370	+	0.0353335i
$879$	6.89079	−	16.6358i	0.232421	−	0.561113i
$880$	25.1004	+	50.1092i	0.846136	+	1.68918i
$881$	2.81079	+	6.78586i	0.0946981	+	0.228621i	0.964130	−	0.265432i	$-0.0855147\pi$
$881$	2.81079	+	6.78586i	0.0946981	+	0.228621i	−0.869431	+	0.494054i	$0.835515\pi$
$882$	−6.34143	−	6.74957i	−0.213527	−	0.227270i
$883$	2.95495	+	9.74118i	0.0994421	+	0.327817i	0.992519	−	0.122086i	$-0.0389585\pi$
$883$	2.95495	+	9.74118i	0.0994421	+	0.327817i	−0.893077	+	0.449903i	$0.851459\pi$
$884$	−0.806683	+	1.30631i	−0.0271317	+	0.0439359i
$885$	37.3715	−	3.68077i	1.25623	−	0.123728i
$886$	−3.03606	−	11.2606i	−0.101999	−	0.378306i
$887$	−4.52336	+	22.7405i	−0.151880	+	0.763550i	0.827491	+	0.561479i	$0.189767\pi$
$887$	−4.52336	+	22.7405i	−0.151880	+	0.763550i	−0.979371	+	0.202072i	$0.935233\pi$
$888$	−24.1833	−	7.21270i	−0.811539	−	0.242042i
$889$	3.07790	−	0.612232i	0.103229	−	0.0205336i
$890$	8.72727	−	25.8419i	0.292539	−	0.866222i
$891$	3.85918	+	1.17067i	0.129287	+	0.0392189i
$892$	15.1582	−	5.19822i	0.507533	−	0.174049i
$893$	−5.70085	−	6.94651i	−0.190772	−	0.232456i
$894$	8.07579	+	12.9419i	0.270095	+	0.432843i
$895$	−23.9526			−0.800649
$896$	4.35954	−	6.22601i	0.145642	−	0.207996i
$897$	1.15408			0.0385336
$898$	13.5142	+	21.6574i	0.450976	+	0.722716i
$899$	0.386634	+	0.471115i	0.0128950	+	0.0157126i
$900$	4.58713	+	13.3762i	0.152904	+	0.445874i
$901$	−26.1757	−	7.94030i	−0.872038	−	0.264530i
$902$	−20.5020	+	60.7075i	−0.682643	+	2.02134i
$903$	−0.896423	+	0.178310i	−0.0298311	+	0.00593377i
$904$	−31.4689	+	17.0100i	−1.04664	+	0.565744i
$905$	2.17374	−	10.9281i	0.0722575	−	0.363263i
$906$	−2.16985	−	8.04783i	−0.0720885	−	0.267371i
$907$	−42.2101	+	4.15733i	−1.40156	+	0.138042i	−0.770377	−	0.637589i	$-0.779932\pi$
$907$	−42.2101	+	4.15733i	−1.40156	+	0.138042i	−0.631187	+	0.775631i	$0.717432\pi$
$908$	−0.507913	−	0.313650i	−0.0168557	−	0.0104089i
$909$	3.30963	+	10.9104i	0.109773	+	0.361875i
$910$	−0.720172	−	0.766523i	−0.0238735	−	0.0254100i
$911$	3.45582	+	8.34310i	0.114497	+	0.276419i	0.970731	−	0.240168i	$-0.0772024\pi$
$911$	3.45582	+	8.34310i	0.114497	+	0.276419i	−0.856235	+	0.516587i	$0.827202\pi$
$912$	−3.53018	+	4.07635i	−0.116896	+	0.134982i
$913$	18.6627	−	45.0557i	0.617645	−	1.49113i
$914$	−47.2557	+	17.8699i	−1.56308	+	0.591083i
$915$	−43.3037	−	23.1463i	−1.43158	−	0.765194i
$916$	1.40065	+	39.0637i	0.0462788	+	1.29070i
$917$	−9.61149	−	7.88794i	−0.317399	−	0.260483i
$918$	−2.07830	−	2.69978i	−0.0685943	−	0.0891061i
$919$	7.17691	+	10.7410i	0.236744	+	0.354313i	0.930750	−	0.365657i	$-0.119156\pi$
$919$	7.17691	+	10.7410i	0.236744	+	0.354313i	−0.694005	+	0.719970i	$0.744156\pi$
$920$	−32.8180	+	13.7737i	−1.08198	+	0.454104i
$921$	−2.80992	−	1.87753i	−0.0925900	−	0.0618666i
$922$	−2.17198	+	2.48447i	−0.0715304	+	0.0818215i
$923$	−1.72394	+	0.921466i	−0.0567442	+	0.0303304i
$924$	4.68412	−	2.72387i	0.154096	−	0.0896087i
$925$	6.18336	−	62.7807i	0.203308	−	2.06422i
$926$	7.08437	−	9.91882i	0.232807	−	0.325953i
$927$	8.90364	−	8.90364i	0.292434	−	0.292434i
$928$	4.28751	−	8.86765i	0.140744	−	0.291095i
$929$	−24.0062	−	24.0062i	−0.787619	−	0.787619i	0.193485	−	0.981103i	$-0.438021\pi$
$929$	−24.0062	−	24.0062i	−0.787619	−	0.787619i	−0.981103	+	0.193485i	$0.938021\pi$
$930$	1.69635	−	0.282784i	0.0556255	−	0.00927284i
$931$	8.78589	+	0.865335i	0.287946	+	0.0283602i
$932$	−23.1184	+	3.11690i	−0.757270	+	0.102097i
$933$	6.80806	+	12.7370i	0.222886	+	0.416990i
$934$	4.04870	+	60.3311i	0.132477	+	1.97409i
$935$	18.7533	−	28.0663i	0.613298	−	0.917865i
$936$	0.179953	+	0.883100i	0.00588196	+	0.0288650i
$937$	−3.56488	+	2.38197i	−0.116459	+	0.0778157i	−0.612436	−	0.790520i	$-0.709810\pi$
$937$	−3.56488	+	2.38197i	−0.116459	+	0.0778157i	0.495976	+	0.868336i	$0.334810\pi$
$938$	−0.0968516	+	0.744622i	−0.00316232	+	0.0243128i
$939$	0.821586	−	1.00110i	0.0268114	−	0.0326698i
$940$	42.1291	−	19.2469i	1.37410	−	0.627764i
$941$	20.9392	−	39.1746i	0.682600	−	1.27705i	−0.267032	−	0.963688i	$-0.586043\pi$
$941$	20.9392	−	39.1746i	0.682600	−	1.27705i	0.949632	−	0.313367i	$-0.101457\pi$
$942$	1.89225	−	4.19365i	0.0616529	−	0.136637i
$943$	−37.5943	−	15.5721i	−1.22424	−	0.507096i
$944$	−40.3682	+	15.4813i	−1.31387	+	0.503874i
$945$	2.15635	−	0.893188i	0.0701460	−	0.0290554i
$946$	−0.241797	+	7.75552i	−0.00786149	+	0.252154i
$947$	21.8121	−	6.61664i	0.708799	−	0.215012i	0.0847560	−	0.996402i	$-0.472989\pi$
$947$	21.8121	−	6.61664i	0.708799	−	0.215012i	0.624043	+	0.781390i	$0.285489\pi$
$948$	−26.8866	+	19.3937i	−0.873237	+	0.629879i
$949$	0.159583	+	1.62027i	0.00518027	+	0.0525962i
$950$	−11.6845	−	6.72181i	−0.379096	−	0.218084i
$951$	−22.0424	−	4.38451i	−0.714775	−	0.142178i
$952$	−4.55777	−	0.427406i	−0.147718	−	0.0138523i
$953$	2.21979	+	11.1596i	0.0719059	+	0.361495i	0.999939	−	0.0110011i	$-0.00350184\pi$
$953$	2.21979	+	11.1596i	0.0719059	+	0.361495i	−0.928034	+	0.372497i	$0.878502\pi$
$954$	−14.3899	+	7.12420i	−0.465890	+	0.230654i
$955$	−0.269301	+	0.887765i	−0.00871437	+	0.0287274i
$956$	7.99635	+	9.06099i	0.258620	+	0.293053i
$957$	5.42808	−	4.45471i	0.175465	−	0.144000i
$958$	32.6640	+	7.56254i	1.05532	+	0.244335i
$959$			9.17330i			0.296221i
$960$	−15.6568	−	22.9646i	−0.505322	−	0.741179i
$961$			30.8775i			0.996048i
$962$	0.906881	−	3.91698i	0.0292390	−	0.126288i
$963$	−12.3138	+	10.1057i	−0.396807	+	0.325651i
$964$	7.74128	+	0.483175i	0.249330	+	0.0155620i
$965$	−3.38496	+	11.1587i	−0.108966	+	0.359212i
$966$	1.52675	+	3.08382i	0.0491223	+	0.0992203i
$967$	8.97546	+	45.1227i	0.288631	+	1.45105i	0.804282	+	0.594248i	$0.202550\pi$
$967$	8.97546	+	45.1227i	0.288631	+	1.45105i	−0.515650	+	0.856799i	$0.672450\pi$
$968$	−4.38829	−	14.2266i	−0.141045	−	0.457260i
$969$	3.18544	+	0.633623i	0.102331	+	0.0203549i
$970$	22.8015	−	39.6357i	0.732111	−	1.27263i
$971$	0.0756746	+	0.768337i	0.00242851	+	0.0246571i	0.996323	−	0.0856811i	$-0.0273066\pi$
$971$	0.0756746	+	0.768337i	0.00242851	+	0.0246571i	−0.993894	+	0.110338i	$0.964807\pi$
$972$	−1.97429	−	0.319642i	−0.0633254	−	0.0102525i
$973$	−2.28871	+	0.694272i	−0.0733727	+	0.0222574i
$974$	−19.6819	−	0.613631i	−0.630650	−	0.0196620i
$975$	−2.08143	+	0.862156i	−0.0666591	+	0.0276111i
$976$	55.1341	+	12.4938i	1.76480	+	0.399916i
$977$	21.2502	+	8.80211i	0.679853	+	0.281604i	0.695765	−	0.718269i	$-0.255065\pi$
$977$	21.2502	+	8.80211i	0.679853	+	0.281604i	−0.0159125	+	0.999873i	$0.505065\pi$
$978$	7.79495	+	3.51722i	0.249255	+	0.112468i
$979$	−10.5535	+	19.7442i	−0.337291	+	0.631028i
$980$	−15.8959	+	42.6368i	−0.507776	+	1.36198i
$981$	−8.50930	+	10.3686i	−0.271681	+	0.331044i
$982$	17.5624	+	2.28432i	0.560440	+	0.0728954i
$983$	8.27384	−	5.52840i	0.263894	−	0.176329i	−0.416583	−	0.909098i	$-0.636772\pi$
$983$	8.27384	−	5.52840i	0.263894	−	0.176329i	0.680477	+	0.732769i	$0.261772\pi$
$984$	6.05372	−	31.1952i	0.192986	−	0.994468i
$985$	−1.55348	+	2.32495i	−0.0494980	+	0.0740790i
$986$	−5.91912	+	0.397220i	−0.188503	+	0.0126501i
$987$	−2.11097	−	3.94934i	−0.0671928	−	0.125709i
$988$	−0.683218	−	0.520878i	−0.0217361	−	0.0165713i
$989$	−4.90385	−	0.482987i	−0.155933	−	0.0153581i
$990$	−3.25816	−	19.5449i	−0.103551	−	0.621179i
$991$	−0.576190	−	0.576190i	−0.0183033	−	0.0183033i	0.697896	−	0.716199i	$-0.254120\pi$
$991$	−0.576190	−	0.576190i	−0.0183033	−	0.0183033i	−0.716199	+	0.697896i	$0.754120\pi$
$992$	−1.79709	+	0.831182i	−0.0570578	+	0.0263901i
$993$	0.774335	−	0.774335i	0.0245728	−	0.0245728i
$994$	−4.74288	−	3.38753i	−0.150435	−	0.107446i
$995$	2.15262	−	21.8560i	0.0682428	−	0.692881i
$996$	−6.18686	+	23.3808i	−0.196038	+	0.740848i
$997$	1.17308	−	0.627022i	0.0371517	−	0.0198580i	−0.452716	−	0.891655i	$-0.649545\pi$
$997$	1.17308	−	0.627022i	0.0371517	−	0.0198580i	0.489868	+	0.871797i	$0.337045\pi$
$998$	0.559889	+	0.489469i	0.0177230	+	0.0154939i
$999$	7.41860	+	4.95695i	0.234714	+	0.156831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.253.28	yes	512
128.85	even	32	inner	384.2.v.a.85.28	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.85.28	✓	512	128.85	even	32	inner
384.2.v.a.253.28	yes	512	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19979 - 0.748670i) q^{2} +(0.634393 + 0.773010i) q^{3} +(0.878985 - 1.79649i) q^{4} +(3.32465 + 1.00852i) q^{5} +(1.33987 + 0.452498i) q^{6} +(-0.658894 + 0.131062i) q^{7} +(-0.290385 - 2.81348i) q^{8} +(-0.195090 + 0.980785i) q^{9} +O(q^{10})\)	\(q+(1.19979 - 0.748670i) q^{2} +(0.634393 + 0.773010i) q^{3} +(0.878985 - 1.79649i) q^{4} +(3.32465 + 1.00852i) q^{5} +(1.33987 + 0.452498i) q^{6} +(-0.658894 + 0.131062i) q^{7} +(-0.290385 - 2.81348i) q^{8} +(-0.195090 + 0.980785i) q^{9} +(4.74393 - 1.27906i) q^{10} +(-4.01341 + 0.395286i) q^{11} +(1.94633 - 0.460218i) q^{12} +(0.0924961 + 0.304919i) q^{13} +(-0.692411 + 0.650541i) q^{14} +(1.32954 + 3.20979i) q^{15} +(-2.45477 - 3.15818i) q^{16} +(-0.921948 + 2.22578i) q^{17} +(0.500218 + 1.32279i) q^{18} +(-1.18894 - 0.635499i) q^{19} +(4.73413 - 5.08624i) q^{20} +(-0.519310 - 0.426187i) q^{21} +(-4.51930 + 3.47898i) q^{22} +(-2.01222 - 3.01150i) q^{23} +(1.99063 - 2.00932i) q^{24} +(5.87886 + 3.92813i) q^{25} +(0.339260 + 0.296589i) q^{26} +(-0.881921 + 0.471397i) q^{27} +(-0.343706 + 1.29890i) q^{28} +(-0.170668 + 1.73283i) q^{29} +(3.99824 + 2.85569i) q^{30} +(0.247500 - 0.247500i) q^{31} +(-5.30964 - 1.95133i) q^{32} +(-2.85164 - 2.85164i) q^{33} +(0.560233 + 3.36070i) q^{34} +(-2.32277 - 0.228773i) q^{35} +(1.59049 + 1.21257i) q^{36} +(-4.20593 - 7.86874i) q^{37} +(-1.90225 + 0.127656i) q^{38} +(-0.177027 + 0.264939i) q^{39} +(1.87203 - 9.64671i) q^{40} +(9.34151 - 6.24180i) q^{41} +(-0.942136 - 0.122542i) q^{42} +(0.863089 - 1.05168i) q^{43} +(-2.81760 + 7.55751i) q^{44} +(-1.63775 + 3.06402i) q^{45} +(-4.66885 - 2.10667i) q^{46} +(6.15840 + 2.55089i) q^{47} +(0.884017 - 3.90109i) q^{48} +(-6.05019 + 2.50607i) q^{49} +(9.99427 + 0.311595i) q^{50} +(-2.30543 + 0.699344i) q^{51} +(0.629087 + 0.101851i) q^{52} +(1.11288 + 11.2993i) q^{53} +(-0.705198 + 1.22584i) q^{54} +(-13.7419 - 2.73342i) q^{55} +(0.560074 + 1.81573i) q^{56} +(-0.263005 - 1.32222i) q^{57} +(1.09255 + 2.20680i) q^{58} +(3.13761 - 10.3433i) q^{59} +(6.93501 + 0.432852i) q^{60} +(-10.9249 + 8.96587i) q^{61} +(0.111652 - 0.482244i) q^{62} -0.671803i q^{63} +(-7.83135 + 1.63398i) q^{64} +1.10703i q^{65} +(-5.55630 - 1.28643i) q^{66} +(0.610952 - 0.501396i) q^{67} +(3.18822 + 3.61270i) q^{68} +(1.05138 - 3.46594i) q^{69} +(-2.95811 + 1.46451i) q^{70} +(1.19682 + 6.01682i) q^{71} +(2.81607 + 0.264078i) q^{72} +(5.01139 + 0.996828i) q^{73} +(-10.9373 - 6.29197i) q^{74} +(0.693025 + 7.03640i) q^{75} +(-2.18673 + 1.57732i) q^{76} +(2.59260 - 0.786458i) q^{77} +(-0.0140425 + 0.450405i) q^{78} +(-15.3139 + 6.34322i) q^{79} +(-4.97617 - 12.9756i) q^{80} +(-0.923880 - 0.382683i) q^{81} +(6.53479 - 14.4825i) q^{82} +(-5.70048 + 10.6648i) q^{83} +(-1.22211 + 0.558325i) q^{84} +(-5.30991 + 6.47014i) q^{85} +(0.248165 - 1.90796i) q^{86} +(-1.44776 + 0.967364i) q^{87} +(2.27756 + 11.1769i) q^{88} +(3.08418 - 4.61580i) q^{89} +(0.328984 + 4.90231i) q^{90} +(-0.100908 - 0.188787i) q^{91} +(-7.17884 + 0.967873i) q^{92} +(0.348333 + 0.0343078i) q^{93} +(9.29856 - 1.55008i) q^{94} +(-3.31188 - 3.31188i) q^{95} +(-1.86000 - 5.34232i) q^{96} +(6.58074 - 6.58074i) q^{97} +(-5.38273 + 7.53636i) q^{98} +(0.395286 - 4.01341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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